LMFDB - Embedded newform 4.43.b.a.3.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4,43,Mod(3,4)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 43, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4.3");

S:= CuspForms(chi, 43);

N := Newforms(S);

Level:	$ N $	$=$	$ 4 = 2^{2} $
Weight:	$ k $	$=$	$ 43 $
Character orbit:	$[\chi]$	$=$	4.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$44.6910828688$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 10 x^{19} + \cdots + 58\!\cdots\!00 $ x^20 - 10x^19 + 5706153082570973323x^18 - 51355377743138759622x^17 + 13343173699766809979413665939112009554x^16 - 106745389598134478671254098668417526292x^15 + 16693561135686664895777023363809349450836742088201197926x^14 - 116854927949806652402394845579312073483103768875776598924x^13 + 12284098900487592120525252537511749903693989702365519944116294471974842357x^12 - 73704593402925551204037451877584023047946172398254928793692285881529570994x^11 + 5516336147855606858523686089551925620872550605204284237709228096232716802903002973392852815x^10 - 27581680739278033616992990920942078185728560285226412785624452693072488043503225695971731566x^9 + 1517878455648890489695001684494985450863656907930075530716193787298253181082685160982376785780193706273465608x^8 - 6071513822595561793289922302311740912247209538248891478546899284872728565602870282822535480605440763098529168x^7 + 247927346162348834423749451228358273830598680827645592402766959253902686957544779014145143897629177833020849983266016607613296x^6 - 743782038487046482020949974600608660820127089359583964963101929666258034682878431219929402460388250614556570989709464530610144x^5 + 21882859534466294287228939036881852886736567554233410610686187918042890793111187503539197126144459328207808614661966382731946870926901879113984x^4 - 43765719068932587334821147262019576155322637135607756862708434377743408992078827726727780310966542756561373742782816017120711348834657134242304x^3 + 797986861806247403230610551033523340880583800155549360507218139622165905339813235339233274528940034896016490666809497848765871357094638184408888034812433039360x^2 - 797986861806247381347751016567229797433683250320173941085258239326107003523949004518061241874365252424389220229742074846265472846643782528368645538242847539200*x + 582776938526821481202155286064003991435776530121314093258912761316091268879815440298128652209601652301637461916981612534140214354747684373258396815504158589037626247741440000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	multiple of $ 2^{380}\cdot 3^{41}\cdot 5^{10}\cdot 7^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			3.9
Root			$0.500000 - 2.73023e7i$ of defining polynomial
Character	$\chi$	$=$	4.3
Dual form			4.43.b.a.3.10

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(85368.2 - 2.09541e6i) q^{2} +4.36838e8i q^{3} +(-4.38347e12 - 3.57763e11i) q^{4} +5.12233e14 q^{5} +(9.15355e14 + 3.72920e13i) q^{6} -3.44914e17i q^{7} +(-1.12387e18 + 9.15464e18i) q^{8} +1.09228e20 q^{9} +O(q^{10})$	\(q+(85368.2 - 2.09541e6i) q^{2} +4.36838e8i q^{3} +(-4.38347e12 - 3.57763e11i) q^{4} +5.12233e14 q^{5} +(9.15355e14 + 3.72920e13i) q^{6} -3.44914e17i q^{7} +(-1.12387e18 + 9.15464e18i) q^{8} +1.09228e20 q^{9} +(4.37284e19 - 1.07334e21i) q^{10} +6.73283e21i q^{11} +(1.56285e20 - 1.91486e21i) q^{12} -3.68714e23 q^{13} +(-7.22737e23 - 2.94447e22i) q^{14} +2.23763e23i q^{15} +(1.90868e25 + 3.13649e24i) q^{16} +2.47874e25 q^{17} +(9.32461e24 - 2.28878e26i) q^{18} +1.02130e27i q^{19} +(-2.24536e27 - 1.83258e26i) q^{20} +1.50671e26 q^{21} +(1.41081e28 + 5.74770e26i) q^{22} +5.89536e28i q^{23} +(-3.99909e27 - 4.90949e26i) q^{24} +3.50090e28 q^{25} +(-3.14765e28 + 7.72609e29i) q^{26} +9.55133e28i q^{27} +(-1.23397e29 + 1.51192e30i) q^{28} +5.42849e29 q^{29} +(4.68875e29 + 1.91022e28i) q^{30} +4.43764e30i q^{31} +(8.20166e30 - 3.97270e31i) q^{32} -2.94115e30 q^{33} +(2.11606e30 - 5.19398e31i) q^{34} -1.76676e32i q^{35} +(-4.78798e32 - 3.90778e31i) q^{36} +2.65529e32 q^{37} +(2.14005e33 + 8.71866e31i) q^{38} -1.61068e32i q^{39} +(-5.75684e32 + 4.68931e33i) q^{40} +2.58682e33 q^{41} +(1.28625e31 - 3.15719e32i) q^{42} +2.21804e34i q^{43} +(2.40876e33 - 2.95132e34i) q^{44} +5.59503e34 q^{45} +(1.23532e35 + 5.03276e33i) q^{46} -1.77561e35i q^{47} +(-1.37014e33 + 8.33784e33i) q^{48} +1.93008e35 q^{49} +(2.98866e33 - 7.33583e34i) q^{50} +1.08281e34i q^{51} +(1.61625e36 + 1.31913e35i) q^{52} +3.00183e36 q^{53} +(2.00140e35 + 8.15380e33i) q^{54} +3.44878e36i q^{55} +(3.15756e36 + 3.87639e35i) q^{56} -4.46143e35 q^{57} +(4.63421e34 - 1.13749e36i) q^{58} -1.17807e37i q^{59} +(8.00541e34 - 9.80857e35i) q^{60} +1.65211e37 q^{61} +(9.29869e36 + 3.78833e35i) q^{62} -3.76743e37i q^{63} +(-8.25444e37 - 2.05773e37i) q^{64} -1.88868e38 q^{65} +(-2.51081e35 + 6.16294e36i) q^{66} +3.76074e38i q^{67} +(-1.08655e38 - 8.86802e36i) q^{68} -2.57531e37 q^{69} +(-3.70210e38 - 1.50825e37i) q^{70} -5.25049e38i q^{71} +(-1.22758e38 + 9.99945e38i) q^{72} -9.87210e38 q^{73} +(2.26677e37 - 5.56393e38i) q^{74} +1.52932e37i q^{75} +(3.65384e38 - 4.47684e39i) q^{76} +2.32225e39 q^{77} +(-3.37505e38 - 1.37501e37i) q^{78} +3.24571e39i q^{79} +(9.77690e39 + 1.60661e39i) q^{80} +1.19099e40 q^{81} +(2.20832e38 - 5.42045e39i) q^{82} +2.03868e40i q^{83} +(-6.60463e38 - 5.39047e37i) q^{84} +1.26969e40 q^{85} +(4.64770e40 + 1.89350e39i) q^{86} +2.37137e38i q^{87} +(-6.16367e40 - 7.56684e39i) q^{88} -3.29345e40 q^{89} +(4.77637e39 - 1.17239e41i) q^{90} +1.27175e41i q^{91} +(2.10914e40 - 2.58421e41i) q^{92} -1.93853e39 q^{93} +(-3.72063e41 - 1.51581e40i) q^{94} +5.23144e41i q^{95} +(1.73543e40 + 3.58279e39i) q^{96} -8.36434e41 q^{97} +(1.64768e40 - 4.04432e41i) q^{98} +7.35415e41i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 802164 q^{2} + 1311168818192 q^{4} + 139235684997000 q^{5} + 68\!\cdots\!12 q^{6}+ \cdots - 73\!\cdots\!76 q^{9}+O(q^{10}) $ 20 * q + 802164 * q^2 + 1311168818192 * q^4 + 139235684997000 * q^5 + 6838718638036512 * q^6 - 27661415389266953664 * q^8 - 733170595646091132876 * q^9	$ 20 q + 802164 q^{2} + 1311168818192 q^{4} + 139235684997000 q^{5} + 68\!\cdots\!12 q^{6}+ \cdots + 18\!\cdots\!96 q^{98}+O(q^{100}) $ 20 * q + 802164 * q^2 + 1311168818192 * q^4 + 139235684997000 * q^5 + 6838718638036512 * q^6 - 27661415389266953664 * q^8 - 733170595646091132876 * q^9 + 42625185369378343240 * q^10 - 25848729272513843675520 * q^12 - 144898631886191567496248 * q^13 - 306990738295992471121728 * q^14 + 27792040878005009897120000 * q^16 + 81746542725793625328399528 * q^17 - 217831601203830755951030124 * q^18 + 6344592401135696008447573920 * q^20 + 7651089590961386749851047424 * q^21 - 46254109397133274566238240800 * q^22 + 506607644284406956508290140672 * q^24 + 844166434154191999887370985820 * q^25 + 305910330554143989456096580488 * q^26 - 1621415041794921570009743366400 * q^28 + 8494173617816210057524981535304 * q^29 + 32483836243012295467926394800960 * q^30 - 117067340157863901568162598132736 * q^32 - 195434629079924022845409037850880 * q^33 - 435728002928020507520645688017048 * q^34 + 905808650859207966395798479569552 * q^36 + 320827308804868360600766816935048 * q^37 - 834801746373065199942054885540960 * q^38 - 2080347678511686114819737054821760 * q^40 + 12238592465130696350192985088255080 * q^41 + 39180793491987624842407723014766080 * q^42 - 40147560736600746149658671246198400 * q^44 - 57674168870802092374169153418160440 * q^45 - 133593585977858896021440512714708928 * q^46 + 223617847456028179696661192651827200 * q^48 - 763663932888918132103393205670102316 * q^49 - 1073296820241355924814923786366326660 * q^50 - 580677968103327319151855528386839392 * q^52 + 3592528655430046000719727125882705672 * q^53 + 8087462166590362832897538370358812224 * q^54 - 4056862272141293872664295528725971968 * q^56 + 1376964140105307936676325853454767360 * q^57 - 17787847411919404506009575679670206968 * q^58 + 27803845757503537955964429994460432640 * q^60 - 72876803820111699199759396563493728440 * q^61 - 83779848218915601601226708273126396160 * q^62 - 51258837764961549702163120437185671168 * q^64 + 143337782114217802520090675036041365840 * q^65 + 479881795533282188176080436671310498560 * q^66 - 201679039132028748396903074185205050848 * q^68 + 496255895990320623770556878095159325184 * q^69 + 244550326432622351468933399511720393600 * q^70 + 1389470702024602675984554222025462031424 * q^72 + 675217186810136917874725959945538619752 * q^73 - 5048325762233564608985375515346235670968 * q^74 - 727730227778639944706768217921060021120 * q^76 - 13945771646073577607404274150247166932480 * q^77 + 2630485389052859541031650397045824087360 * q^78 - 14080069438753558698176635521889841825280 * q^80 + 50326416439524122225413610454605570342484 * q^81 + 38442316210858292795461617709768475559208 * q^82 + 21041665749991691364416236667734761560064 * q^84 - 100747029416581567610441680879732008651760 * q^85 - 109399875737541346773887857542693387248928 * q^86 + 61542411942227832459784035156153652876800 * q^88 + 298677519739918601751826215340976530195944 * q^89 + 5248331693055749298139854308097091987080 * q^90 - 311056321102768653749854891753699429405440 * q^92 - 902946967697899772252214392286633142732800 * q^93 - 120754391334239789606838050760853185629568 * q^94 - 369891338439189821551415861997759233875968 * q^96 + 2729077788738058742150638081801454021515048 * q^97 + 1829330555781863715528793474157579946873396 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/4\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	85368.2	−	2.09541e6i	0.0407067	−	0.999171i
$2$	85368.2	−	2.09541e6i	0.0407067	−	0.999171i
$3$			4.36838e8i			0.0417613i	0.999782	+	0.0208806i	$0.00664699\pi$
$3$			4.36838e8i			0.0417613i	−0.999782	+	0.0208806i	$0.993353\pi$
$4$	−4.38347e12	−	3.57763e11i	−0.996686	−	0.0813460i
$5$	5.12233e14			1.07423			0.537115	−	0.843509i	$-0.319514\pi$
$5$	5.12233e14			1.07423			0.537115	+	0.843509i	$0.319514\pi$
$6$	9.15355e14	+	3.72920e13i	0.0417266	+	0.00169996i
$7$		−	3.44914e17i		−	0.617521i	−0.951140	−	0.308760i	$-0.900086\pi$
$7$		−	3.44914e17i		−	0.617521i	0.951140	−	0.308760i	$-0.0999141\pi$
$8$	−1.12387e18	+	9.15464e18i	−0.121850	+	0.992548i
$9$	1.09228e20			0.998256
$10$	4.37284e19	−	1.07334e21i	0.0437284	−	1.07334i
$11$			6.73283e21i			0.909812i	0.890540	+	0.454906i	$0.150327\pi$
$11$			6.73283e21i			0.909812i	−0.890540	+	0.454906i	$0.849673\pi$
$12$	1.56285e20	−	1.91486e21i	0.00339711	−	0.0416229i
$13$	−3.68714e23			−1.49238			−0.746190	−	0.665733i	$-0.768119\pi$
$13$	−3.68714e23			−1.49238			−0.746190	+	0.665733i	$0.768119\pi$
$14$	−7.22737e23	−	2.94447e22i	−0.617009	−	0.0251373i
$15$			2.23763e23i			0.0448612i
$16$	1.90868e25	+	3.13649e24i	0.986766	+	0.162153i
$17$	2.47874e25			0.358760			0.179380	−	0.983780i	$-0.442591\pi$
$17$	2.47874e25			0.358760			0.179380	+	0.983780i	$0.442591\pi$
$18$	9.32461e24	−	2.28878e26i	0.0406357	−	0.997429i
$19$			1.02130e27i			1.42997i	0.699138	+	0.714987i	$0.253567\pi$
$19$			1.02130e27i			1.42997i	−0.699138	+	0.714987i	$0.746433\pi$
$20$	−2.24536e27	−	1.83258e26i	−1.07067	−	0.0873843i
$21$	1.50671e26			0.0257884
$22$	1.41081e28	+	5.74770e26i	0.909058	+	0.0370355i
$23$			5.89536e28i			1.49357i	0.665066	+	0.746785i	$0.268404\pi$
$23$			5.89536e28i			1.49357i	−0.665066	+	0.746785i	$0.731596\pi$
$24$	−3.99909e27	−	4.90949e26i	−0.0414501	−	0.00508863i
$25$	3.50090e28			0.153971
$26$	−3.14765e28	+	7.72609e29i	−0.0607499	+	1.49114i
$27$			9.55133e28i			0.0834497i
$28$	−1.23397e29	+	1.51192e30i	−0.0502328	+	0.615474i
$29$	5.42849e29			0.105760			0.0528800	−	0.998601i	$-0.483160\pi$
$29$	5.42849e29			0.105760			0.0528800	+	0.998601i	$0.483160\pi$
$30$	4.68875e29	+	1.91022e28i	0.0448240	+	0.00182615i
$31$			4.43764e30i			0.213087i	0.994308	+	0.106543i	$0.0339783\pi$
$31$			4.43764e30i			0.213087i	−0.994308	+	0.106543i	$0.966022\pi$
$32$	8.20166e30	−	3.97270e31i	0.202186	−	0.979347i
$33$	−2.94115e30			−0.0379949
$34$	2.11606e30	−	5.19398e31i	0.0146039	−	0.358462i
$35$		−	1.76676e32i		−	0.663360i
$36$	−4.78798e32	−	3.90778e31i	−0.994948	−	0.0812041i
$37$	2.65529e32			0.310367			0.155184	−	0.987886i	$-0.450403\pi$
$37$	2.65529e32			0.310367			0.155184	+	0.987886i	$0.450403\pi$
$38$	2.14005e33	+	8.71866e31i	1.42879	+	0.0582096i
$39$		−	1.61068e32i		−	0.0623237i
$40$	−5.75684e32	+	4.68931e33i	−0.130895	+	1.06623i
$41$	2.58682e33			0.350191			0.175095	−	0.984551i	$-0.443977\pi$
$41$	2.58682e33			0.350191			0.175095	+	0.984551i	$0.443977\pi$
$42$	1.28625e31	−	3.15719e32i	0.00104976	−	0.0257671i
$43$			2.21804e34i			1.10441i	0.833708	+	0.552206i	$0.186214\pi$
$43$			2.21804e34i			1.10441i	−0.833708	+	0.552206i	$0.813786\pi$
$44$	2.40876e33	−	2.95132e34i	0.0740095	−	0.906797i
$45$	5.59503e34			1.07236
$46$	1.23532e35	+	5.03276e33i	1.49233	+	0.0607984i
$47$		−	1.77561e35i		−	1.36550i	−0.730651	−	0.682751i	$-0.760783\pi$
$47$		−	1.77561e35i		−	1.36550i	0.730651	−	0.682751i	$-0.239217\pi$
$48$	−1.37014e33	+	8.33784e33i	−0.00677171	+	0.0412086i
$49$	1.93008e35			0.618668
$50$	2.98866e33	−	7.33583e34i	0.00626767	−	0.153844i
$51$			1.08281e34i			0.0149823i
$52$	1.61625e36	+	1.31913e35i	1.48743	+	0.121399i
$53$	3.00183e36			1.85180			0.925899	−	0.377772i	$-0.123310\pi$
$53$	3.00183e36			1.85180			0.925899	+	0.377772i	$0.123310\pi$
$54$	2.00140e35	+	8.15380e33i	0.0833805	+	0.00339696i
$55$			3.44878e36i			0.977348i
$56$	3.15756e36	+	3.87639e35i	0.612919	+	0.0752451i
$57$	−4.46143e35			−0.0597175
$58$	4.63421e34	−	1.13749e36i	0.00430514	−	0.105672i
$59$		−	1.17807e37i		−	0.764329i	−0.924094	−	0.382164i	$-0.875179\pi$
$59$		−	1.17807e37i		−	0.764329i	0.924094	−	0.382164i	$-0.124821\pi$
$60$	8.00541e34	−	9.80857e35i	0.00364928	−	0.0447125i
$61$	1.65211e37			0.532245			0.266122	−	0.963939i	$-0.414257\pi$
$61$	1.65211e37			0.532245			0.266122	+	0.963939i	$0.414257\pi$
$62$	9.29869e36	+	3.78833e35i	0.212910	+	0.00867407i
$63$		−	3.76743e37i		−	0.616444i
$64$	−8.25444e37	−	2.05773e37i	−0.970305	−	0.241885i
$65$	−1.88868e38			−1.60316
$66$	−2.51081e35	+	6.16294e36i	−0.00154665	+	0.0379634i
$67$			3.76074e38i			1.68928i	0.535331	+	0.844642i	$0.320187\pi$
$67$			3.76074e38i			1.68928i	−0.535331	+	0.844642i	$0.679813\pi$
$68$	−1.08655e38	−	8.86802e36i	−0.357571	−	0.0291837i
$69$	−2.57531e37			−0.0623734
$70$	−3.70210e38	−	1.50825e37i	−0.662810	−	0.0270032i
$71$		−	5.25049e38i		−	0.697871i	−0.937147	−	0.348935i	$-0.886543\pi$
$71$		−	5.25049e38i		−	0.697871i	0.937147	−	0.348935i	$-0.113457\pi$
$72$	−1.22758e38	+	9.99945e38i	−0.121638	+	0.990817i
$73$	−9.87210e38			−0.732200			−0.366100	−	0.930576i	$-0.619307\pi$
$73$	−9.87210e38			−0.732200			−0.366100	+	0.930576i	$0.619307\pi$
$74$	2.26677e37	−	5.56393e38i	0.0126340	−	0.310110i
$75$			1.52932e37i			0.00643003i
$76$	3.65384e38	−	4.47684e39i	0.116323	−	1.42523i
$77$	2.32225e39			0.561828
$78$	−3.37505e38	−	1.37501e37i	−0.0622720	−	0.00253699i
$79$			3.24571e39i			0.458291i	0.973392	+	0.229145i	$0.0735932\pi$
$79$			3.24571e39i			0.458291i	−0.973392	+	0.229145i	$0.926407\pi$
$80$	9.77690e39	+	1.60661e39i	1.06001	+	0.174189i
$81$	1.19099e40			0.994771
$82$	2.20832e38	−	5.42045e39i	0.0142551	−	0.349900i
$83$			2.03868e40i			1.02025i	0.860099	+	0.510127i	$0.170402\pi$
$83$			2.03868e40i			1.02025i	−0.860099	+	0.510127i	$0.829598\pi$
$84$	−6.60463e38	−	5.39047e37i	−0.0257030	−	0.00209779i
$85$	1.26969e40			0.385390
$86$	4.64770e40	+	1.89350e39i	1.10350	+	0.0449570i
$87$			2.37137e38i			0.00441667i
$88$	−6.16367e40	−	7.56684e39i	−0.903032	−	0.110861i
$89$	−3.29345e40			−0.380593			−0.190297	−	0.981727i	$-0.560945\pi$
$89$	−3.29345e40			−0.380593			−0.190297	+	0.981727i	$0.560945\pi$
$90$	4.77637e39	−	1.17239e41i	0.0436522	−	1.07147i
$91$			1.27175e41i			0.921576i
$92$	2.10914e40	−	2.58421e41i	0.121496	−	1.48862i
$93$	−1.93853e39			−0.00889877
$94$	−3.72063e41	−	1.51581e40i	−1.36437	−	0.0555851i
$95$			5.23144e41i			1.53612i
$96$	1.73543e40	+	3.58279e39i	0.0408988	+	0.00844356i
$97$	−8.36434e41			−1.58571			−0.792857	−	0.609407i	$-0.791408\pi$
$97$	−8.36434e41			−1.58571			−0.792857	+	0.609407i	$0.791408\pi$
$98$	1.64768e40	−	4.04432e41i	0.0251840	−	0.618155i
$99$			7.35415e41i			0.908225i
$100$	−1.53461e41	−	1.25249e40i	−0.153461	−	0.0125249i
$101$	1.29748e42			1.05281			0.526407	−	0.850233i	$-0.323539\pi$
$101$	1.29748e42			1.05281			0.526407	+	0.850233i	$0.323539\pi$
$102$	2.26893e40	+	9.24372e38i	0.0149698	+	0.000609879i
$103$			2.53262e42i			1.36141i	0.732559	+	0.680703i	$0.238326\pi$
$103$			2.53262e42i			1.36141i	−0.732559	+	0.680703i	$0.761674\pi$
$104$	4.14388e41	−	3.37545e42i	0.181847	−	1.48126i
$105$	7.71788e40			0.0277027
$106$	2.56261e41	−	6.29009e42i	0.0753806	−	1.85026i
$107$			4.74067e42i			1.14493i	0.819928	+	0.572466i	$0.194013\pi$
$107$			4.74067e42i			1.14493i	−0.819928	+	0.572466i	$0.805987\pi$
$108$	3.41712e40	−	4.18680e41i	0.00678830	−	0.0831731i
$109$	2.65480e42			0.434586			0.217293	−	0.976106i	$-0.430277\pi$
$109$	2.65480e42			0.434586			0.217293	+	0.976106i	$0.430277\pi$
$110$	7.22662e42	+	2.94416e41i	0.976537	+	0.0397846i
$111$			1.15993e41i			0.0129613i
$112$	1.08182e42	−	6.58331e42i	0.100133	−	0.609348i
$113$	1.73993e43			1.33624			0.668122	−	0.744052i	$-0.267099\pi$
$113$	1.73993e43			1.33624			0.668122	+	0.744052i	$0.267099\pi$
$114$	−3.80864e40	+	9.34853e41i	−0.00243090	+	0.0596680i
$115$			3.01980e43i			1.60444i
$116$	−2.37956e42	−	1.94212e41i	−0.105409	−	0.00860315i
$117$	−4.02740e43			−1.48978
$118$	−2.46855e43	−	1.00570e42i	−0.763695	−	0.0311133i
$119$		−	8.54951e42i		−	0.221541i
$120$	−2.04847e42	−	2.51480e41i	−0.0445269	−	0.00546636i
$121$	9.43264e42			0.172243
$122$	1.41037e42	−	3.46185e43i	0.0216660	−	0.531804i
$123$			1.13002e42i			0.0146244i
$124$	1.58763e42	−	1.94523e43i	0.0173338	−	0.212381i
$125$	−9.85355e43			−0.908830
$126$	−7.89432e43	−	3.21619e42i	−0.615933	−	0.0250934i
$127$		−	2.04142e44i		−	1.34913i	−0.738214	−	0.674567i	$-0.764330\pi$
$127$		−	2.04142e44i		−	1.34913i	0.738214	−	0.674567i	$-0.235670\pi$
$128$	−5.01646e43	+	1.71208e44i	−0.281182	+	0.959654i
$129$	−9.68922e42			−0.0461216
$130$	−1.61233e43	+	3.95756e44i	−0.0652594	+	1.60183i
$131$		−	1.89626e44i		−	0.653433i	−0.945122	−	0.326717i	$-0.894058\pi$
$131$		−	1.89626e44i		−	0.653433i	0.945122	−	0.326717i	$-0.105942\pi$
$132$	1.28925e43	+	1.05224e42i	0.0378690	+	0.00309073i
$133$	3.52261e44			0.883038
$134$	7.88031e44	+	3.21048e43i	1.68788	+	0.0687652i
$135$			4.89251e43i			0.0896442i
$136$	−2.78578e43	+	2.26920e44i	−0.0437150	+	0.356086i
$137$	2.66812e44			0.358982			0.179491	−	0.983760i	$-0.442555\pi$
$137$	2.66812e44			0.358982			0.179491	+	0.983760i	$0.442555\pi$
$138$	−2.19850e42	+	5.39635e43i	−0.00253902	+	0.0623217i
$139$		−	1.43080e45i		−	1.41994i	−0.704233	−	0.709969i	$-0.748709\pi$
$139$		−	1.43080e45i		−	1.41994i	0.704233	−	0.709969i	$-0.251291\pi$
$140$	−6.32083e43	+	7.74455e44i	−0.0539616	+	0.661161i
$141$	7.75653e43			0.0570251
$142$	−1.10020e45	−	4.48225e43i	−0.697292	−	0.0284080i
$143$		−	2.48249e45i		−	1.35779i
$144$	2.08482e45	+	3.42593e44i	0.985045	+	0.161870i
$145$	2.78065e44			0.113611
$146$	−8.42764e43	+	2.06861e45i	−0.0298055	+	0.731593i
$147$			8.43132e43i			0.0258364i
$148$	−1.16394e45	−	9.49966e43i	−0.309339	−	0.0252471i
$149$	−5.44921e45			−1.25725			−0.628626	−	0.777708i	$-0.716382\pi$
$149$	−5.44921e45			−1.25725			−0.628626	+	0.777708i	$0.716382\pi$
$150$	3.20457e43	+	1.30556e42i	0.00642470	+	0.000261746i
$151$			8.47244e45i			1.47738i	0.674045	+	0.738691i	$0.264556\pi$
$151$			8.47244e45i			1.47738i	−0.674045	+	0.738691i	$0.735444\pi$
$152$	−9.34964e45	−	1.14781e45i	−1.41932	−	0.174243i
$153$	2.70748e45			0.358134
$154$	1.98246e44	−	4.86607e45i	0.0228702	−	0.561362i
$155$			2.27311e45i			0.228904i
$156$	−5.76243e43	+	7.06038e44i	−0.00506978	+	0.0621172i
$157$	−9.20987e45			−0.708534			−0.354267	−	0.935144i	$-0.615270\pi$
$157$	−9.20987e45			−0.708534			−0.354267	+	0.935144i	$0.615270\pi$
$158$	6.80111e45	+	2.77081e44i	0.457911	+	0.0186555i
$159$			1.31131e45i			0.0773334i
$160$	4.20116e45	−	2.03495e46i	0.217195	−	1.05204i
$161$	2.03339e46			0.922310
$162$	1.01673e45	−	2.49562e46i	0.0404939	−	0.993947i
$163$			1.50437e46i			0.526521i	0.964725	+	0.263261i	$0.0847979\pi$
$163$			1.50437e46i			0.526521i	−0.964725	+	0.263261i	$0.915202\pi$
$164$	−1.13392e46	−	9.25468e44i	−0.349030	−	0.0284866i
$165$	−1.50656e45			−0.0408153
$166$	4.27187e46	+	1.74038e45i	1.01941	+	0.0415312i
$167$			4.33313e46i			0.911498i	0.890108	+	0.455749i	$0.150629\pi$
$167$			4.33313e46i			0.911498i	−0.890108	+	0.455749i	$0.849371\pi$
$168$	−1.69335e44	+	1.37934e45i	−0.00314233	+	0.0255963i
$169$	7.49094e46			1.22720
$170$	1.08391e45	−	2.66053e46i	0.0156880	−	0.385071i
$171$			1.11555e47i			1.42748i
$172$	7.93532e45	−	9.72270e46i	0.0898395	−	1.10075i
$173$	−6.25068e46			−0.626555			−0.313278	−	0.949662i	$-0.601427\pi$
$173$	−6.25068e46			−0.626555			−0.313278	+	0.949662i	$0.601427\pi$
$174$	4.96900e44	+	2.02439e43i	0.00441301	+	0.000179788i
$175$		−	1.20751e46i		−	0.0950804i
$176$	−2.11175e46	+	1.28508e47i	−0.147529	+	0.897771i
$177$	5.14627e45			0.0319193
$178$	−2.81156e45	+	6.90115e46i	−0.0154927	+	0.380278i
$179$		−	3.80072e47i		−	1.86188i	−0.365169	−	0.930941i	$-0.618989\pi$
$179$		−	3.80072e47i		−	1.86188i	0.365169	−	0.930941i	$-0.381011\pi$
$180$	−2.45256e47	−	2.00170e46i	−1.06880	−	0.0872319i
$181$	−3.46498e47			−1.34416			−0.672080	−	0.740478i	$-0.734599\pi$
$181$	−3.46498e47			−1.34416			−0.672080	+	0.740478i	$0.734599\pi$
$182$	2.66483e47	+	1.08567e46i	0.920812	+	0.0375143i
$183$			7.21702e45i			0.0222272i
$184$	−5.39699e47	−	6.62562e46i	−1.48244	−	0.181992i
$185$	1.36013e47			0.333406
$186$	−1.65489e44	+	4.06202e45i	−0.000362240	+	0.00889140i
$187$			1.66889e47i			0.326404i
$188$	−6.35248e46	+	7.78333e47i	−0.111078	+	1.36098i
$189$	3.29438e46			0.0515319
$190$	1.09620e48	+	4.46599e46i	1.53485	+	0.0625305i
$191$		−	1.08717e48i		−	1.36331i	−0.731673	−	0.681656i	$-0.761260\pi$
$191$		−	1.08717e48i		−	1.36331i	0.731673	−	0.681656i	$-0.238740\pi$
$192$	8.98893e45	−	3.60585e46i	0.0101014	−	0.0405212i
$193$	−1.71620e47			−0.172928			−0.0864638	−	0.996255i	$-0.527557\pi$
$193$	−1.71620e47			−0.172928			−0.0864638	+	0.996255i	$0.527557\pi$
$194$	−7.14048e46	+	1.75267e48i	−0.0645493	+	1.58440i
$195$		−	8.25045e46i		−	0.0669500i
$196$	−8.46045e47	−	6.90512e46i	−0.616618	−	0.0503262i
$197$	1.83199e48			1.19987			0.599933	−	0.800050i	$-0.295194\pi$
$197$	1.83199e48			1.19987			0.599933	+	0.800050i	$0.295194\pi$
$198$	1.54100e48	+	6.27811e46i	0.907472	+	0.0369709i
$199$		−	2.60559e48i		−	1.38036i	−0.723640	−	0.690178i	$-0.757532\pi$
$199$		−	2.60559e48i		−	1.38036i	0.723640	−	0.690178i	$-0.242468\pi$
$200$	−3.93456e46	+	3.20495e47i	−0.0187615	+	0.152824i
$201$	−1.64283e47			−0.0705466
$202$	1.10763e47	−	2.71875e48i	0.0428566	−	1.05194i
$203$		−	1.87236e47i		−	0.0653089i
$204$	3.87389e45	−	4.74645e46i	0.00121875	−	0.0149326i
$205$	1.32505e48			0.376186
$206$	5.30688e48	+	2.16205e47i	1.36028	+	0.0554184i
$207$			6.43939e48i			1.49097i
$208$	−7.03759e48	−	1.15647e48i	−1.47263	−	0.241994i
$209$	−6.87625e48			−1.30101
$210$	6.58861e45	−	1.61721e47i	0.00112769	−	0.0276798i
$211$			1.29416e48i			0.200473i	0.994964	+	0.100236i	$0.0319599\pi$
$211$			1.29416e48i			0.200473i	−0.994964	+	0.100236i	$0.968040\pi$
$212$	−1.31585e49	−	1.07395e48i	−1.84566	−	0.150636i
$213$	2.29361e47			0.0291440
$214$	9.93366e48	+	4.04702e47i	1.14398	+	0.0466065i
$215$			1.13615e49i			1.18639i
$216$	−8.74390e47	−	1.07345e47i	−0.0828279	−	0.0101684i
$217$	1.53060e48			0.131585
$218$	2.26636e47	−	5.56291e48i	0.0176906	−	0.434226i
$219$		−	4.31251e47i		−	0.0305776i
$220$	1.23385e48	−	1.51176e49i	0.0795033	−	0.974109i
$221$	−9.13947e48			−0.535406
$222$	2.43054e47	+	9.90212e45i	0.0129506	+	0.000527613i
$223$		−	2.48990e47i		−	0.0120720i	−0.999982	−	0.00603601i	$-0.998079\pi$
$223$		−	2.48990e47i		−	0.0120720i	0.999982	−	0.00603601i	$-0.00192133\pi$
$224$	−1.37024e49	−	2.82886e48i	−0.604767	−	0.124854i
$225$	3.82397e48			0.153703
$226$	1.48535e48	−	3.64588e49i	0.0543941	−	1.33514i
$227$			3.50753e49i			1.17073i	0.810769	+	0.585367i	$0.199050\pi$
$227$			3.50753e49i			1.17073i	−0.810769	+	0.585367i	$0.800950\pi$
$228$	1.95565e48	+	1.59613e47i	0.0595196	+	0.00485778i
$229$	3.93952e49			1.09370			0.546851	−	0.837230i	$-0.315827\pi$
$229$	3.93952e49			1.09370			0.546851	+	0.837230i	$0.315827\pi$
$230$	6.32772e49	+	2.57795e48i	1.60311	+	0.0653114i
$231$			1.01444e48i			0.0234626i
$232$	−6.10093e47	+	4.96959e48i	−0.0128869	+	0.104972i
$233$	3.05096e49			0.588792			0.294396	−	0.955684i	$-0.404882\pi$
$233$	3.05096e49			0.588792			0.294396	+	0.955684i	$0.404882\pi$
$234$	−3.43812e48	+	8.43907e49i	−0.0606440	+	1.48854i
$235$		−	9.09525e49i		−	1.46686i
$236$	−4.21472e48	+	5.16405e49i	−0.0621751	+	0.761796i
$237$	−1.41785e48			−0.0191388
$238$	−1.79148e49	−	7.29856e47i	−0.221358	−	0.00901823i
$239$		−	1.32965e48i		−	0.0150446i	−0.999972	−	0.00752230i	$-0.997606\pi$
$239$		−	1.32965e48i		−	0.0150446i	0.999972	−	0.00752230i	$-0.00239444\pi$
$240$	−7.01830e47	+	4.27092e48i	−0.00727437	+	0.0442675i
$241$	−1.74106e50			−1.65369			−0.826847	−	0.562427i	$-0.809868\pi$
$241$	−1.74106e50			−1.65369			−0.826847	+	0.562427i	$0.809868\pi$
$242$	8.05247e47	−	1.97653e49i	0.00701143	−	0.172100i
$243$			1.56537e49i			0.124993i
$244$	−7.24196e49	−	5.91063e48i	−0.530481	−	0.0432960i
$245$	9.88651e49			0.664592
$246$	2.36786e48	+	9.64677e46i	0.0146123	+	0.000595312i
$247$		−	3.76568e50i		−	2.13407i
$248$	−4.06250e49	−	4.98734e48i	−0.211499	−	0.0259647i
$249$	−8.90571e48			−0.0426071
$250$	−8.41180e48	+	2.06473e50i	−0.0369955	+	0.908077i
$251$			8.48990e49i			0.343364i	0.985152	+	0.171682i	$0.0549201\pi$
$251$			8.48990e49i			0.343364i	−0.985152	+	0.171682i	$0.945080\pi$
$252$	−1.34785e49	+	1.65144e50i	−0.0501452	+	0.614401i
$253$	−3.96925e50			−1.35887
$254$	−4.27763e50	−	1.74273e49i	−1.34802	−	0.0549188i
$255$			5.54649e48i			0.0160944i
$256$	3.54469e50	+	1.19731e50i	0.947413	+	0.320014i
$257$	3.02776e50			0.745635			0.372818	−	0.927905i	$-0.378392\pi$
$257$	3.02776e50			0.745635			0.372818	+	0.927905i	$0.378392\pi$
$258$	−8.27151e47	+	2.03029e49i	−0.00187746	+	0.0460834i
$259$		−	9.15846e49i		−	0.191658i
$260$	8.27896e50	+	6.75699e49i	1.59785	+	0.130411i
$261$	5.92944e49			0.105575
$262$	−3.97345e50	−	1.61881e49i	−0.652892	−	0.0265991i
$263$			5.97625e50i			0.906480i	0.891389	+	0.453240i	$0.149732\pi$
$263$			5.97625e50i			0.906480i	−0.891389	+	0.453240i	$0.850268\pi$
$264$	3.30548e48	−	2.69252e49i	0.00462969	−	0.0377118i
$265$	1.53764e51			1.98926
$266$	3.00719e49	−	7.38132e50i	0.0359456	−	0.882306i
$267$		−	1.43870e49i		−	0.0158941i
$268$	1.34546e50	−	1.64851e51i	0.137416	−	1.68369i
$269$	−1.33476e51			−1.26068			−0.630341	−	0.776318i	$-0.717085\pi$
$269$	−1.33476e51			−1.26068			−0.630341	+	0.776318i	$0.717085\pi$
$270$	1.02518e50	+	4.17664e48i	0.0895699	+	0.00364912i
$271$			1.16035e51i			0.938069i	0.883180	+	0.469034i	$0.155398\pi$
$271$			1.16035e51i			0.938069i	−0.883180	+	0.469034i	$0.844602\pi$
$272$	4.73113e50	+	7.77454e49i	0.354012	+	0.0581739i
$273$	−5.55546e49			−0.0384862
$274$	2.27772e49	−	5.59081e50i	0.0146130	−	0.358685i
$275$			2.35710e50i			0.140085i
$276$	1.12888e50	+	9.21353e48i	0.0621667	+	0.00507382i
$277$	8.00292e50			0.408483			0.204241	−	0.978921i	$-0.434527\pi$
$277$	8.00292e50			0.408483			0.204241	+	0.978921i	$0.434527\pi$
$278$	−2.99813e51	−	1.22145e50i	−1.41876	−	0.0578010i
$279$			4.84715e50i			0.212715i
$280$	1.61741e51	+	1.98561e50i	0.658417	+	0.0808306i
$281$	−2.00427e51			−0.757049			−0.378525	−	0.925591i	$-0.623568\pi$
$281$	−2.00427e51			−0.757049			−0.378525	+	0.925591i	$0.623568\pi$
$282$	6.62161e48	−	1.62531e50i	0.00232130	−	0.0569778i
$283$			3.60507e51i			1.17327i	0.809851	+	0.586636i	$0.199548\pi$
$283$			3.60507e51i			1.17327i	−0.809851	+	0.586636i	$0.800452\pi$
$284$	−1.87844e50	+	2.30154e51i	−0.0567690	+	0.695558i
$285$	−2.28529e50			−0.0641504
$286$	−5.20185e51	−	2.11926e50i	−1.35666	−	0.0552710i
$287$		−	8.92228e50i		−	0.216250i
$288$	8.95852e50	−	4.33931e51i	0.201834	−	0.977639i
$289$	−4.15928e51			−0.871292
$290$	2.37379e49	−	5.82662e50i	0.00462471	−	0.113516i
$291$		−	3.65386e50i		−	0.0662215i
$292$	4.32741e51	+	3.53188e50i	0.729773	+	0.0595615i
$293$	4.99766e51			0.784416			0.392208	−	0.919877i	$-0.371711\pi$
$293$	4.99766e51			0.784416			0.392208	+	0.919877i	$0.371711\pi$
$294$	1.76671e50	+	7.19766e48i	0.0258150	+	0.00105171i
$295$		−	6.03448e51i		−	0.821065i
$296$	−2.98421e50	+	2.43082e51i	−0.0378184	+	0.308055i
$297$	−6.43075e50			−0.0759235
$298$	−4.65189e50	+	1.14184e52i	−0.0511786	+	1.25621i
$299$		−	2.17370e52i		−	2.22898i
$300$	5.47136e48	−	6.70375e49i	0.000523057	−	0.00640872i
$301$	7.65031e51			0.681997
$302$	1.77533e52	+	7.23277e50i	1.47616	+	0.0601394i
$303$			5.66787e50i			0.0439668i
$304$	−3.20330e51	+	1.94934e52i	−0.231874	+	1.41105i
$305$	8.46264e51			0.571754
$306$	2.31133e50	−	5.67329e51i	0.0145785	−	0.357837i
$307$			2.04292e52i			1.20322i	0.798790	+	0.601610i	$0.205474\pi$
$307$			2.04292e52i			1.20322i	−0.798790	+	0.601610i	$0.794526\pi$
$308$	−1.01795e52	−	8.30815e50i	−0.559966	−	0.0457024i
$309$	−1.10634e51			−0.0568541
$310$	4.76310e51	+	1.94051e50i	0.228715	+	0.00931795i
$311$		−	1.38112e52i		−	0.619815i	−0.950767	−	0.309907i	$-0.899702\pi$
$311$		−	1.38112e52i		−	0.619815i	0.950767	−	0.309907i	$-0.100298\pi$
$312$	1.47452e51	+	1.81020e50i	0.0618593	+	0.00759417i
$313$	−2.00021e52			−0.784594			−0.392297	−	0.919839i	$-0.628319\pi$
$313$	−2.00021e52			−0.784594			−0.392297	+	0.919839i	$0.628319\pi$
$314$	−7.86230e50	+	1.92985e52i	−0.0288421	+	0.707947i
$315$		−	1.92980e52i		−	0.662203i
$316$	1.16120e51	−	1.42275e52i	0.0372801	−	0.456772i
$317$	−6.03842e51			−0.181417			−0.0907086	−	0.995877i	$-0.528913\pi$
$317$	−6.03842e51			−0.181417			−0.0907086	+	0.995877i	$0.528913\pi$
$318$	2.74775e51	+	1.11945e50i	0.0772693	+	0.00314799i
$319$			3.65491e51i			0.0962216i
$320$	−4.22820e52	−	1.05404e52i	−1.04233	−	0.259840i
$321$	−2.07090e51			−0.0478138
$322$	1.73587e51	−	4.26079e52i	0.0375442	−	0.921546i
$323$			2.53154e52i			0.513017i
$324$	−5.22068e52	−	4.26093e51i	−0.991474	−	0.0809206i
$325$	−1.29083e52			−0.229784
$326$	3.15228e52	+	1.28426e51i	0.526085	+	0.0214330i
$327$			1.15972e51i			0.0181489i
$328$	−2.90725e51	+	2.36814e52i	−0.0426709	+	0.347581i
$329$	−6.12432e52			−0.843225
$330$	−1.28612e50	+	3.15686e51i	−0.00166146	+	0.0407814i
$331$			9.15916e52i			1.11037i	0.831727	+	0.555185i	$0.187353\pi$
$331$			9.15916e52i			1.11037i	−0.831727	+	0.555185i	$0.812647\pi$
$332$	7.29364e51	−	8.93648e52i	0.0829936	−	1.01687i
$333$	2.90033e52			0.309826
$334$	9.07970e52	+	3.69912e51i	0.910743	+	0.0371041i
$335$			1.92638e53i			1.81468i
$336$	2.87584e51	+	4.72579e50i	0.0254471	+	0.00418167i
$337$	2.30190e53			1.91363			0.956815	−	0.290697i	$-0.0938872\pi$
$337$	2.30190e53			1.91363			0.956815	+	0.290697i	$0.0938872\pi$
$338$	6.39488e51	−	1.56966e53i	0.0499553	−	1.22618i
$339$			7.60069e51i			0.0558032i
$340$	−5.56566e52	−	4.54249e51i	−0.384113	−	0.0313500i
$341$	−2.98779e52			−0.193869
$342$	2.33753e53	+	9.52323e51i	1.42630	+	0.0581080i
$343$		−	1.74175e53i		−	0.999561i
$344$	−2.03053e53	−	2.49279e52i	−1.09618	−	0.134573i
$345$	−1.31916e52			−0.0670034
$346$	−5.33610e51	+	1.30978e53i	−0.0255050	+	0.626036i
$347$		−	1.13625e53i		−	0.511159i	−0.966788	−	0.255579i	$-0.917734\pi$
$347$		−	1.13625e53i		−	0.511159i	0.966788	−	0.255579i	$-0.0822662\pi$
$348$	8.48389e49	−	1.03948e51i	0.000359278	−	0.00440203i
$349$	−1.59361e53			−0.635401			−0.317700	−	0.948191i	$-0.602911\pi$
$349$	−1.59361e53			−0.635401			−0.317700	+	0.948191i	$0.602911\pi$
$350$	−2.53023e52	−	1.03083e51i	−0.0950016	−	0.00387041i
$351$		−	3.52171e52i		−	0.124539i
$352$	2.67476e53	+	5.52204e52i	0.891021	+	0.183952i
$353$	1.47758e53			0.463748			0.231874	−	0.972746i	$-0.425514\pi$
$353$	1.47758e53			0.463748			0.231874	+	0.972746i	$0.425514\pi$
$354$	4.39328e50	−	1.07836e52i	0.00129933	−	0.0318929i
$355$		−	2.68948e53i		−	0.749674i
$356$	1.44368e53	+	1.17828e52i	0.379332	+	0.0309597i
$357$	3.73475e51			0.00925185
$358$	−7.96408e53	−	3.24461e52i	−1.86034	−	0.0757912i
$359$			4.16185e53i			0.916859i	0.888731	+	0.458430i	$0.151588\pi$
$359$			4.16185e53i			0.916859i	−0.888731	+	0.458430i	$0.848412\pi$
$360$	−6.28809e52	+	5.12205e53i	−0.130667	+	1.06437i
$361$	−5.32960e53			−1.04482
$362$	−2.95799e52	+	7.26058e53i	−0.0547164	+	1.34305i
$363$			4.12053e51i			0.00719307i
$364$	4.54984e52	−	5.57466e53i	0.0749665	−	0.918522i
$365$	−5.05682e53			−0.786552
$366$	1.51226e52	+	6.16104e50i	0.0222088	+	0.000904798i
$367$		−	1.14758e54i		−	1.59146i	−0.605654	−	0.795728i	$-0.707089\pi$
$367$		−	1.14758e54i		−	1.59146i	0.605654	−	0.795728i	$-0.292911\pi$
$368$	−1.84907e53	+	1.12524e54i	−0.242187	+	1.47380i
$369$	2.82553e53			0.349580
$370$	1.16112e52	−	2.85003e53i	0.0135719	−	0.333130i
$371$		−	1.03537e54i		−	1.14352i
$372$	8.49748e51	+	6.93534e50i	0.00886928	+	0.000723879i
$373$	1.05831e54			1.04406			0.522032	−	0.852926i	$-0.325174\pi$
$373$	1.05831e54			1.04406			0.522032	+	0.852926i	$0.325174\pi$
$374$	3.49702e53	+	1.42471e52i	0.326133	+	0.0132868i
$375$		−	4.30440e52i		−	0.0379539i
$376$	1.62551e54	+	1.99556e53i	1.35533	+	0.166387i
$377$	−2.00156e53			−0.157834
$378$	2.81236e51	−	6.90310e52i	0.00209770	−	0.0514892i
$379$			1.17738e54i			0.830790i	0.909641	+	0.415395i	$0.136357\pi$
$379$			1.17738e54i			0.830790i	−0.909641	+	0.415395i	$0.863643\pi$
$380$	1.87162e53	−	2.29319e54i	0.124957	−	1.53103i
$381$	8.91771e52			0.0563415
$382$	−2.27806e54	−	9.28095e52i	−1.36218	−	0.0554960i
$383$			3.00595e53i			0.170140i	0.996375	+	0.0850701i	$0.0271114\pi$
$383$			3.00595e53i			0.170140i	−0.996375	+	0.0850701i	$0.972889\pi$
$384$	−7.47901e52	−	2.19138e52i	−0.0400764	−	0.0117425i
$385$	1.18953e54			0.603532
$386$	−1.46509e52	+	3.59615e53i	−0.00703931	+	0.172784i
$387$			2.42272e54i			1.10249i
$388$	3.66648e54	+	2.99245e53i	1.58046	+	0.128992i
$389$	8.02760e53			0.327827			0.163913	−	0.986475i	$-0.447588\pi$
$389$	8.02760e53			0.327827			0.163913	+	0.986475i	$0.447588\pi$
$390$	−1.72881e53	−	7.04326e51i	−0.0668945	−	0.00272532i
$391$			1.46131e54i			0.535833i
$392$	−2.16916e53	+	1.76692e54i	−0.0753850	+	0.614058i
$393$	8.28359e52			0.0272882
$394$	1.56394e53	−	3.83878e54i	0.0488426	−	1.19887i
$395$			1.66256e54i			0.492310i
$396$	2.63105e53	−	3.22367e54i	0.0738805	−	0.905215i
$397$	−2.58264e54			−0.687802			−0.343901	−	0.939006i	$-0.611748\pi$
$397$	−2.58264e54			−0.687802			−0.343901	+	0.939006i	$0.611748\pi$
$398$	−5.45978e54	−	2.22434e53i	−1.37921	−	0.0561898i
$399$			1.53881e53i			0.0368768i
$400$	6.68211e53	+	1.09805e53i	0.151934	+	0.0249669i
$401$	−7.59329e54			−1.63832			−0.819159	−	0.573566i	$-0.805560\pi$
$401$	−7.59329e54			−1.63832			−0.819159	+	0.573566i	$0.805560\pi$
$402$	−1.40246e52	+	3.44242e53i	−0.00287172	+	0.0704882i
$403$		−	1.63622e54i		−	0.318007i
$404$	−5.68746e54	−	4.64190e53i	−1.04932	−	0.0856421i
$405$	6.10065e54			1.06861
$406$	−3.92337e53	−	1.59840e52i	−0.0652548	−	0.00265851i
$407$			1.78776e54i			0.282376i
$408$	−9.91271e52	−	1.21694e52i	−0.0148706	−	0.00182559i
$409$	6.95905e53			0.0991655			0.0495828	−	0.998770i	$-0.484211\pi$
$409$	6.95905e53			0.0991655			0.0495828	+	0.998770i	$0.484211\pi$
$410$	1.13117e53	−	2.77653e54i	0.0153133	−	0.375874i
$411$			1.16553e53i			0.0149915i
$412$	9.06078e53	−	1.11017e55i	0.110745	−	1.35689i
$413$	−4.06334e54			−0.471989
$414$	1.34932e55	+	5.49719e53i	1.48973	+	0.0606923i
$415$			1.04428e55i			1.09599i
$416$	−3.02407e54	+	1.46479e55i	−0.301739	+	1.46156i
$417$	6.25029e53			0.0592984
$418$	−5.87013e53	+	1.44086e55i	−0.0529597	+	1.29993i
$419$		−	1.56072e55i		−	1.33915i	−0.742742	−	0.669577i	$-0.766475\pi$
$419$		−	1.56072e55i		−	1.33915i	0.742742	−	0.669577i	$-0.233525\pi$
$420$	−3.38311e53	−	2.76117e52i	−0.0276109	−	0.00225351i
$421$	1.33852e55			1.03920			0.519601	−	0.854409i	$-0.326081\pi$
$421$	1.33852e55			1.03920			0.519601	+	0.854409i	$0.326081\pi$
$422$	2.71180e54	+	1.10480e53i	0.200307	+	0.00816060i
$423$		−	1.93946e55i		−	1.36312i
$424$	−3.37368e54	+	2.74807e55i	−0.225642	+	1.83800i
$425$	8.67782e53			0.0552386
$426$	1.95802e52	−	4.80607e53i	0.00118636	−	0.0291198i
$427$		−	5.69834e54i		−	0.328672i
$428$	1.69604e54	−	2.07806e55i	0.0931357	−	1.14114i
$429$	1.08445e54			0.0567028
$430$	2.38071e55	+	9.69912e53i	1.18541	+	0.0482942i
$431$		−	8.56701e54i		−	0.406263i	−0.979152	−	0.203131i	$-0.934888\pi$
$431$		−	8.56701e54i		−	0.406263i	0.979152	−	0.203131i	$-0.0651118\pi$
$432$	−2.99577e53	+	1.82305e54i	−0.0135316	+	0.0823453i
$433$	2.41905e55			1.04087			0.520437	−	0.853900i	$-0.325769\pi$
$433$	2.41905e55			1.04087			0.520437	+	0.853900i	$0.325769\pi$
$434$	1.30665e53	−	3.20725e54i	0.00535641	−	0.131476i
$435$			1.21469e53i			0.00474452i
$436$	−1.16373e55	−	9.49792e53i	−0.433146	−	0.0353518i
$437$	−6.02093e55			−2.13577
$438$	−9.03648e53	−	3.68151e52i	−0.0305522	−	0.00124471i
$439$		−	2.05801e55i		−	0.663272i	−0.943407	−	0.331636i	$-0.892399\pi$
$439$		−	2.05801e55i		−	0.663272i	0.943407	−	0.331636i	$-0.107601\pi$
$440$	−3.15724e55	−	3.87599e54i	−0.970065	−	0.119090i
$441$	2.10819e55			0.617589
$442$	−7.80220e53	+	1.91510e55i	−0.0217946	+	0.534962i
$443$			3.96202e55i			1.05545i	0.849415	+	0.527726i	$0.176955\pi$
$443$			3.96202e55i			1.05545i	−0.849415	+	0.527726i	$0.823045\pi$
$444$	4.14981e52	−	5.08452e53i	0.00105435	−	0.0129184i
$445$	−1.68702e55			−0.408845
$446$	−5.21738e53	−	2.12558e52i	−0.0120620	−	0.000491413i
$447$		−	2.38042e54i		−	0.0525044i
$448$	−7.09739e54	+	2.84707e55i	−0.149369	+	0.599183i
$449$	−1.65868e55			−0.333111			−0.166555	−	0.986032i	$-0.553264\pi$
$449$	−1.65868e55			−0.333111			−0.166555	+	0.986032i	$0.553264\pi$
$450$	3.26445e53	−	8.01280e54i	0.00625673	−	0.153575i
$451$			1.74166e55i			0.318608i
$452$	−7.62695e55	−	6.22485e54i	−1.33182	−	0.108698i
$453$	−3.70108e54			−0.0616973
$454$	7.34972e55	+	2.99431e54i	1.16976	+	0.0476568i
$455$			6.51430e55i			0.989985i
$456$	5.01407e53	−	4.08428e54i	0.00727660	−	0.0592725i
$457$	1.53796e55			0.213160			0.106580	−	0.994304i	$-0.466010\pi$
$457$	1.53796e55			0.213160			0.106580	+	0.994304i	$0.466010\pi$
$458$	3.36310e54	−	8.25493e55i	0.0445210	−	1.09279i
$459$			2.36753e54i			0.0299384i
$460$	1.08037e55	−	1.32372e56i	0.130515	−	1.59912i
$461$	3.05451e55			0.352551			0.176275	−	0.984341i	$-0.443595\pi$
$461$	3.05451e55			0.352551			0.176275	+	0.984341i	$0.443595\pi$
$462$	2.12568e54	+	8.66013e52i	0.0234432	+	0.000955087i
$463$			6.91151e55i			0.728404i	0.931320	+	0.364202i	$0.118658\pi$
$463$			6.91151e55i			0.728404i	−0.931320	+	0.364202i	$0.881342\pi$
$464$	1.03613e55	+	1.70264e54i	0.104360	+	0.0171493i
$465$	−9.92978e53			−0.00955933
$466$	2.60455e54	−	6.39302e55i	0.0239678	−	0.588304i
$467$		−	1.48679e54i		−	0.0130796i	−0.999979	−	0.00653982i	$-0.997918\pi$
$467$		−	1.48679e54i		−	0.0130796i	0.999979	−	0.00653982i	$-0.00208170\pi$
$468$	1.76540e56	+	1.44086e55i	1.48484	+	0.121187i
$469$	1.29713e56			1.04317
$470$	−1.90583e56	−	7.76446e54i	−1.46565	−	0.0597112i
$471$		−	4.02322e54i		−	0.0295893i
$472$	1.07848e56	+	1.32400e55i	0.758633	+	0.0931337i
$473$	−1.49337e56			−1.00481
$474$	−1.21039e53	+	2.97098e54i	−0.000779078	+	0.0191229i
$475$			3.57547e55i			0.220175i
$476$	−3.05870e54	+	3.74765e55i	−0.0180215	+	0.220807i
$477$	3.27885e56			1.84857
$478$	−2.78616e54	−	1.13510e53i	−0.0150321	−	0.000612416i
$479$		−	1.22376e55i		−	0.0631902i	−0.999501	−	0.0315951i	$-0.989941\pi$
$479$		−	1.22376e55i		−	0.0631902i	0.999501	−	0.0315951i	$-0.0100587\pi$
$480$	8.88943e54	+	1.83522e54i	0.0439347	+	0.00907033i
$481$	−9.79044e55			−0.463186
$482$	−1.48631e55	+	3.64824e56i	−0.0673165	+	1.65232i
$483$			8.88261e54i			0.0385168i
$484$	−4.13477e55	−	3.37465e54i	−0.171672	−	0.0140112i
$485$	−4.28449e56			−1.70342
$486$	3.28009e55	+	1.33633e54i	0.124889	+	0.00508804i
$487$		−	3.22918e56i		−	1.17756i	−0.808293	−	0.588781i	$-0.799608\pi$
$487$		−	3.22918e56i		−	1.17756i	0.808293	−	0.588781i	$-0.200392\pi$
$488$	−1.85676e55	+	1.51244e56i	−0.0648543	+	0.528279i
$489$	−6.57166e54			−0.0219882
$490$	8.43994e54	−	2.07163e56i	0.0270534	−	0.664041i
$491$		−	1.95480e56i		−	0.600330i	−0.953887	−	0.300165i	$-0.902958\pi$
$491$		−	1.95480e56i		−	0.600330i	0.953887	−	0.300165i	$-0.0970417\pi$
$492$	4.04279e53	−	4.95340e54i	0.00118964	−	0.0145759i
$493$	1.34558e55			0.0379424
$494$	−7.89066e56	−	3.21470e55i	−2.13230	−	0.0868708i
$495$			3.76704e56i			0.975643i
$496$	−1.39186e55	+	8.47004e55i	−0.0345526	+	0.210267i
$497$	−1.81097e56			−0.430950
$498$	−7.60264e53	+	1.86611e55i	−0.00173440	+	0.0425718i
$499$		−	6.71315e56i		−	1.46830i	−0.678987	−	0.734151i	$-0.737581\pi$
$499$		−	6.71315e56i		−	1.46830i	0.678987	−	0.734151i	$-0.262419\pi$
$500$	4.31928e56	+	3.52524e55i	0.905818	+	0.0739297i
$501$	−1.89287e55			−0.0380653
$502$	1.77898e56	+	7.24767e54i	0.343079	+	0.0139772i
$503$		−	6.44989e56i		−	1.19296i	−0.802629	−	0.596479i	$-0.796566\pi$
$503$		−	6.44989e56i		−	1.19296i	0.802629	−	0.596479i	$-0.203434\pi$
$504$	3.44895e56	+	4.23411e55i	0.611850	+	0.0751139i
$505$	6.64611e56			1.13096
$506$	−3.38847e55	+	8.31721e56i	−0.0553151	+	1.35774i
$507$			3.27232e55i			0.0512494i
$508$	−7.30347e55	+	8.94852e56i	−0.109747	+	1.34466i
$509$	−5.03698e56			−0.726267			−0.363134	−	0.931737i	$-0.618293\pi$
$509$	−5.03698e56			−0.726267			−0.363134	+	0.931737i	$0.618293\pi$
$510$	1.16222e55	+	4.73494e53i	0.0160811	+	0.000655150i
$511$			3.40502e56i			0.452149i
$512$	2.81147e56	−	7.32539e56i	0.358314	−	0.933601i
$513$	−9.75478e55			−0.119331
$514$	2.58475e55	−	6.34442e56i	0.0303524	−	0.745017i
$515$			1.29729e57i			1.46246i
$516$	4.24724e55	+	3.46645e54i	0.0459688	+	0.00375181i
$517$	1.19549e57			1.24235
$518$	−1.91908e56	−	7.81842e54i	−0.191499	−	0.00780178i
$519$		−	2.73053e55i		−	0.0261657i
$520$	2.12263e56	−	1.72902e57i	0.195346	−	1.59121i
$521$	9.23599e56			0.816378			0.408189	−	0.912898i	$-0.366161\pi$
$521$	9.23599e56			0.816378			0.408189	+	0.912898i	$0.366161\pi$
$522$	5.06186e54	−	1.24246e56i	0.00429763	−	0.105488i
$523$			6.63332e56i			0.540998i	0.962720	+	0.270499i	$0.0871887\pi$
$523$			6.63332e56i			0.540998i	−0.962720	+	0.270499i	$0.912811\pi$
$524$	−6.78413e55	+	8.31221e56i	−0.0531542	+	0.651268i
$525$	5.27485e54			0.00397068
$526$	1.25227e57	+	5.10182e55i	0.905729	+	0.0368998i
$527$			1.09998e56i			0.0764469i
$528$	−5.61373e55	−	9.22491e54i	−0.0374921	−	0.00616098i
$529$	−1.91752e57			−1.23075
$530$	1.31265e56	−	3.22199e57i	0.0809762	−	1.98761i
$531$		−	1.28679e57i		−	0.762996i
$532$	−1.54412e57	−	1.26026e56i	−0.880112	−	0.0718316i
$533$	−9.53796e56			−0.522618
$534$	−3.01468e55	−	1.22820e54i	−0.0158809	−	0.000646995i
$535$			2.42833e57i			1.22992i
$536$	−3.44283e57	−	4.22659e56i	−1.67670	−	0.205840i
$537$	1.66030e56			0.0777546
$538$	−1.13946e56	+	2.79688e57i	−0.0513183	+	1.25964i
$539$			1.29949e57i			0.562872i
$540$	1.75036e55	−	2.14462e56i	0.00729220	−	0.0893471i
$541$	−2.08407e57			−0.835161			−0.417580	−	0.908640i	$-0.637122\pi$
$541$	−2.08407e57			−0.835161			−0.417580	+	0.908640i	$0.637122\pi$
$542$	2.43142e57	+	9.90572e55i	0.937291	+	0.0381857i
$543$		−	1.51364e56i		−	0.0561338i
$544$	2.03298e56	−	9.84730e56i	0.0725363	−	0.351350i
$545$	1.35988e57			0.466846
$546$	−4.74260e54	+	1.16410e56i	−0.00156665	+	0.0384543i
$547$			9.67762e56i			0.307634i	0.988099	+	0.153817i	$0.0491567\pi$
$547$			9.67762e56i			0.307634i	−0.988099	+	0.153817i	$0.950843\pi$
$548$	−1.16956e57	−	9.54555e55i	−0.357792	−	0.0292018i
$549$	1.80457e57			0.531317
$550$	4.93910e56	+	2.01221e55i	0.139969	+	0.00570240i
$551$			5.54412e56i			0.151234i
$552$	2.89432e55	−	2.35761e56i	0.00760022	−	0.0619086i
$553$	1.11949e57			0.283004
$554$	6.83195e55	−	1.67694e57i	0.0166280	−	0.408144i
$555$			5.94155e55i			0.0139235i
$556$	−5.11889e56	+	6.27189e57i	−0.115506	+	1.41523i
$557$	−4.23210e57			−0.919595			−0.459798	−	0.888024i	$-0.652078\pi$
$557$	−4.23210e57			−0.919595			−0.459798	+	0.888024i	$0.652078\pi$
$558$	1.01568e57	+	4.13793e55i	0.212539	+	0.00865894i
$559$		−	8.17822e57i		−	1.64820i
$560$	5.54143e56	−	3.37219e57i	0.107566	−	0.654580i
$561$	−7.29036e55			−0.0136310
$562$	−1.71101e56	+	4.19978e57i	−0.0308170	+	0.756422i
$563$		−	6.17481e57i		−	1.07139i	−0.844412	−	0.535694i	$-0.820050\pi$
$563$		−	6.17481e57i		−	1.07139i	0.844412	−	0.535694i	$-0.179950\pi$
$564$	−3.40005e56	−	2.77500e55i	−0.0568361	−	0.00463876i
$565$	8.91252e57			1.43543
$566$	7.55411e57	+	3.07758e56i	1.17230	+	0.0477601i
$567$		−	4.10789e57i		−	0.614292i
$568$	4.80664e57	+	5.90088e56i	0.692670	+	0.0850358i
$569$	3.94188e57			0.547452			0.273726	−	0.961808i	$-0.411744\pi$
$569$	3.94188e57			0.547452			0.273726	+	0.961808i	$0.411744\pi$
$570$	−1.95091e55	+	4.78863e56i	−0.00261135	+	0.0640972i
$571$		−	2.69658e57i		−	0.347901i	−0.984754	−	0.173951i	$-0.944347\pi$
$571$		−	2.69658e57i		−	0.347901i	0.984754	−	0.173951i	$-0.0556533\pi$
$572$	−8.88145e56	+	1.08819e58i	−0.110450	+	1.35329i
$573$	4.74915e56			0.0569337
$574$	−1.86959e57	−	7.61679e55i	−0.216071	−	0.00880283i
$575$			2.06391e57i			0.229967i
$576$	−9.01618e57	−	2.24762e57i	−0.968613	−	0.241463i
$577$	−1.20517e58			−1.24840			−0.624201	−	0.781264i	$-0.714575\pi$
$577$	−1.20517e58			−1.24840			−0.624201	+	0.781264i	$0.714575\pi$
$578$	−3.55070e56	+	8.71541e57i	−0.0354674	+	0.870569i
$579$		−	7.49700e55i		−	0.00722167i
$580$	−1.21889e57	−	9.94816e55i	−0.113234	−	0.00924176i
$581$	7.03168e57			0.630028
$582$	−7.65634e56	−	3.11923e55i	−0.0661666	−	0.00269566i
$583$			2.02109e58i			1.68479i
$584$	1.10950e57	−	9.03756e57i	0.0892189	−	0.726744i
$585$	−2.06297e58			−1.60037
$586$	4.26641e56	−	1.04722e58i	0.0319310	−	0.783766i
$587$		−	5.08433e57i		−	0.367141i	−0.983007	−	0.183571i	$-0.941234\pi$
$587$		−	5.08433e57i		−	0.367141i	0.983007	−	0.183571i	$-0.0587656\pi$
$588$	3.01642e55	−	3.69584e56i	0.00210168	−	0.0257507i
$589$	−4.53216e57			−0.304708
$590$	−1.26447e58	−	5.15153e56i	−0.820385	−	0.0334229i
$591$			8.00283e56i			0.0501079i
$592$	5.06811e57	+	8.32830e56i	0.306260	+	0.0503269i
$593$	1.75072e58			1.02110			0.510551	−	0.859848i	$-0.329441\pi$
$593$	1.75072e58			1.02110			0.510551	+	0.859848i	$0.329441\pi$
$594$	−5.48982e55	+	1.34751e57i	−0.00309060	+	0.0758606i
$595$		−	4.37934e57i		−	0.237987i
$596$	2.38865e58	+	1.94953e57i	1.25308	+	0.102272i
$597$	1.13822e57			0.0576454
$598$	−4.55481e58	−	1.85565e57i	−2.22713	−	0.0907343i
$599$		−	2.48650e58i		−	1.17388i	−0.809630	−	0.586941i	$-0.800332\pi$
$599$		−	2.48650e58i		−	1.17388i	0.809630	−	0.586941i	$-0.199668\pi$
$600$	−1.40004e56	−	1.71876e55i	−0.00638212	−	0.000783502i
$601$	−1.37669e58			−0.605999			−0.302999	−	0.952991i	$-0.597988\pi$
$601$	−1.37669e58			−0.605999			−0.302999	+	0.952991i	$0.597988\pi$
$602$	6.53093e56	−	1.60306e58i	0.0277619	−	0.681432i
$603$			4.10779e58i			1.68634i
$604$	3.03113e57	−	3.71387e58i	0.120179	−	1.47249i
$605$	4.83171e57			0.185028
$606$	1.18765e57	+	4.83856e55i	0.0439304	+	0.00178975i
$607$			1.75565e58i			0.627299i	0.949539	+	0.313650i	$0.101552\pi$
$607$			1.75565e58i			0.627299i	−0.949539	+	0.313650i	$0.898448\pi$
$608$	4.05733e58	+	8.37636e57i	1.40044	+	0.289121i
$609$	8.17917e55			0.00272738
$610$	7.22440e56	−	1.77327e58i	0.0232742	−	0.571280i
$611$			6.54692e58i			2.03785i
$612$	−1.18682e58	−	9.68638e56i	−0.356947	−	0.0291328i
$613$	2.26722e58			0.658907			0.329454	−	0.944172i	$-0.393135\pi$
$613$	2.26722e58			0.658907			0.329454	+	0.944172i	$0.393135\pi$
$614$	4.28075e58	+	1.74400e57i	1.20222	+	0.0489791i
$615$			5.78833e56i			0.0157100i
$616$	−2.60991e57	+	2.12593e58i	−0.0684589	+	0.557641i
$617$	5.79612e58			1.46943			0.734715	−	0.678376i	$-0.237316\pi$
$617$	5.79612e58			1.46943			0.734715	+	0.678376i	$0.237316\pi$
$618$	−9.44465e55	+	2.31824e57i	−0.00231434	+	0.0568069i
$619$		−	6.98577e58i		−	1.65467i	−0.561711	−	0.827334i	$-0.689857\pi$
$619$		−	6.98577e58i		−	1.65467i	0.561711	−	0.827334i	$-0.310143\pi$
$620$	8.13234e56	−	9.96409e57i	0.0186204	−	0.228146i
$621$	−5.63085e57			−0.124638
$622$	−2.89401e58	−	1.17903e57i	−0.619301	−	0.0252306i
$623$			1.13596e58i			0.235024i
$624$	5.05189e56	−	3.07428e57i	0.0101060	−	0.0614989i
$625$	−5.84333e58			−1.13026
$626$	−1.70754e57	+	4.19127e58i	−0.0319382	+	0.783943i
$627$		−	3.00380e57i		−	0.0543317i
$628$	4.03712e58	+	3.29495e57i	0.706186	+	0.0576364i
$629$	6.58178e57			0.111347
$630$	−4.04373e58	−	1.64744e57i	−0.661654	−	0.0269561i
$631$		−	3.09274e58i		−	0.489471i	−0.969590	−	0.244735i	$-0.921299\pi$
$631$		−	3.09274e58i		−	0.489471i	0.969590	−	0.244735i	$-0.0787011\pi$
$632$	−2.97134e58	−	3.64777e57i	−0.454876	−	0.0558429i
$633$	−5.65337e56			−0.00837200
$634$	−5.15489e56	+	1.26530e58i	−0.00738490	+	0.181267i
$635$		−	1.04568e59i		−	1.44928i
$636$	4.69140e56	−	5.74811e57i	0.00629076	−	0.0770771i
$637$	−7.11648e58			−0.923289
$638$	7.65855e57	+	3.12013e56i	0.0961419	+	0.00391687i
$639$		−	5.73502e58i		−	0.696654i
$640$	−2.56960e58	+	8.76984e58i	−0.302055	+	1.03089i
$641$	−3.35194e58			−0.381309			−0.190655	−	0.981657i	$-0.561061\pi$
$641$	−3.35194e58			−0.381309			−0.190655	+	0.981657i	$0.561061\pi$
$642$	−1.76789e56	+	4.33939e57i	−0.00194635	+	0.0477742i
$643$			1.97548e58i			0.210495i	0.994446	+	0.105247i	$0.0335634\pi$
$643$			1.97548e58i			0.210495i	−0.994446	+	0.105247i	$0.966437\pi$
$644$	−8.91330e58	−	7.27472e57i	−0.919254	−	0.0750262i
$645$	−4.96314e57			−0.0495453
$646$	5.30462e58	+	2.16113e57i	0.512592	+	0.0208832i
$647$			1.03630e59i			0.969382i	0.874686	+	0.484691i	$0.161068\pi$
$647$			1.03630e59i			0.969382i	−0.874686	+	0.484691i	$0.838932\pi$
$648$	−1.33852e58	+	1.09031e59i	−0.121213	+	0.987358i
$649$	7.93177e58			0.695395
$650$	−1.10196e57	+	2.70483e58i	−0.00935374	+	0.229593i
$651$			6.68625e56i			0.00549518i
$652$	5.38210e57	−	6.59437e58i	0.0428304	−	0.524776i
$653$	−2.34394e58			−0.180621			−0.0903107	−	0.995914i	$-0.528786\pi$
$653$	−2.34394e58			−0.180621			−0.0903107	+	0.995914i	$0.528786\pi$
$654$	2.43009e57	+	9.90030e55i	0.0181338	+	0.000738781i
$655$		−	9.71328e58i		−	0.701938i
$656$	4.93741e58	+	8.11353e57i	0.345556	+	0.0567844i
$657$	−1.07831e59			−0.730923
$658$	−5.22822e57	+	1.28330e59i	−0.0343250	+	0.842527i
$659$		−	8.47978e58i		−	0.539251i	−0.962965	−	0.269625i	$-0.913100\pi$
$659$		−	8.47978e58i		−	0.539251i	0.962965	−	0.269625i	$-0.0868999\pi$
$660$	6.60395e57	+	5.38991e56i	0.0406800	+	0.00332016i
$661$	1.73387e59			1.03463			0.517315	−	0.855795i	$-0.326932\pi$
$661$	1.73387e59			1.03463			0.517315	+	0.855795i	$0.326932\pi$
$662$	1.91922e59	+	7.81901e57i	1.10945	+	0.0451995i
$663$		−	3.99246e57i		−	0.0223592i
$664$	−1.86634e59	−	2.29121e58i	−1.01265	−	0.124318i
$665$	1.80439e59			0.948587
$666$	2.47596e57	−	6.07738e58i	0.0126120	−	0.309569i
$667$			3.20029e58i			0.157960i
$668$	1.55024e58	−	1.89942e59i	0.0741467	−	0.908478i
$669$	1.08768e56			0.000504143
$670$	4.03656e59	+	1.64451e58i	1.81318	+	0.0738697i
$671$			1.11234e59i			0.484243i
$672$	1.23575e57	−	5.98572e57i	0.00521407	−	0.0252558i
$673$	−3.47379e59			−1.42065			−0.710325	−	0.703874i	$-0.751452\pi$
$673$	−3.47379e59			−1.42065			−0.710325	+	0.703874i	$0.751452\pi$
$674$	1.96509e58	−	4.82343e59i	0.0778976	−	1.91204i
$675$			3.34382e57i			0.0128489i
$676$	−3.28363e59	−	2.67998e58i	−1.22313	−	0.0998278i
$677$	4.91516e59			1.77491			0.887454	−	0.460896i	$-0.152472\pi$
$677$	4.91516e59			1.77491			0.887454	+	0.460896i	$0.152472\pi$
$678$	1.59266e58	+	6.48857e56i	0.0557570	+	0.00227157i
$679$			2.88497e59i			0.979212i
$680$	−1.42697e58	+	1.16236e59i	−0.0469600	+	0.382519i
$681$	−1.53222e58			−0.0488913
$682$	−2.55062e57	+	6.26065e58i	−0.00789177	+	0.193708i
$683$			5.80952e59i			1.74303i	0.490368	+	0.871516i	$0.336862\pi$
$683$			5.80952e59i			1.74303i	−0.490368	+	0.871516i	$0.663138\pi$
$684$	3.99102e58	−	4.88997e59i	0.116120	−	1.42275i
$685$	1.36670e59			0.385630
$686$	−3.64969e59	−	1.48690e58i	−0.998733	−	0.0406889i
$687$			1.72093e58i			0.0456743i
$688$	−6.95685e58	+	4.23353e59i	−0.179084	+	1.08980i
$689$	−1.10682e60			−2.76359
$690$	−1.12614e57	+	2.76419e58i	−0.00272749	+	0.0669478i
$691$			1.98597e59i			0.466589i	0.972406	+	0.233294i	$0.0749506\pi$
$691$			1.98597e59i			0.466589i	−0.972406	+	0.233294i	$0.925049\pi$
$692$	2.73997e59	+	2.23627e58i	0.624479	+	0.0509677i
$693$	2.53655e59			0.560848
$694$	−2.38092e59	−	9.69998e57i	−0.510735	−	0.0208076i
$695$		−	7.32905e59i		−	1.52534i
$696$	−2.17090e57	−	2.66511e56i	−0.00438376	−	0.000538173i
$697$	6.41204e58			0.125634
$698$	−1.36043e58	+	3.33927e59i	−0.0258651	+	0.634874i
$699$			1.33277e58i			0.0245887i
$700$	−4.32002e57	+	5.29308e58i	−0.00773441	+	0.0947653i
$701$	−6.54657e58			−0.113746			−0.0568729	−	0.998381i	$-0.518113\pi$
$701$	−6.54657e58			−0.113746			−0.0568729	+	0.998381i	$0.518113\pi$
$702$	−7.37944e58	−	3.00642e57i	−0.124435	−	0.00506956i
$703$			2.71185e59i			0.443817i
$704$	1.38543e59	−	5.55758e59i	0.220070	−	0.882795i
$705$	3.97315e58			0.0612581
$706$	1.26138e58	−	3.09614e59i	0.0188777	−	0.463364i
$707$		−	4.47518e59i		−	0.650134i
$708$	−2.25585e58	−	1.84115e57i	−0.0318135	−	0.00259651i
$709$	3.45383e59			0.472857			0.236428	−	0.971649i	$-0.424023\pi$
$709$	3.45383e59			0.472857			0.236428	+	0.971649i	$0.424023\pi$
$710$	−5.63557e59	−	2.29596e58i	−0.749053	−	0.0305168i
$711$			3.54523e59i			0.457492i
$712$	3.70142e58	−	3.01504e59i	0.0463755	−	0.377757i
$713$	−2.61615e59			−0.318260
$714$	3.18829e56	−	7.82584e57i	0.000376613	−	0.00924418i
$715$		−	1.27161e60i		−	1.45857i
$716$	−1.35976e59	+	1.66603e60i	−0.151457	+	1.85571i
$717$	5.80840e56			0.000628281
$718$	8.72079e59	+	3.55289e58i	0.916100	+	0.0373224i
$719$		−	5.25275e59i		−	0.535896i	−0.963433	−	0.267948i	$-0.913655\pi$
$719$		−	5.25275e59i		−	0.535896i	0.963433	−	0.267948i	$-0.0863455\pi$
$720$	1.06791e60	+	1.75488e59i	1.05817	+	0.173886i
$721$	8.73534e59			0.840697
$722$	−4.54978e58	+	1.11677e60i	−0.0425314	+	1.04396i
$723$		−	7.60559e58i		−	0.0690603i
$724$	1.51887e60	+	1.23964e59i	1.33971	+	0.109342i
$725$	1.90046e58			0.0162840
$726$	8.63422e57	+	3.51762e56i	0.00718710	+	0.000292806i
$727$		−	4.38917e59i		−	0.354944i	−0.984126	−	0.177472i	$-0.943208\pi$
$727$		−	4.38917e59i		−	0.354944i	0.984126	−	0.177472i	$-0.0567919\pi$
$728$	−1.16424e60	−	1.42928e59i	−0.914709	−	0.112294i
$729$	1.29633e60			0.989551
$730$	−4.31692e58	+	1.05961e60i	−0.0320179	+	0.785900i
$731$			5.49793e59i			0.396218i
$732$	2.58199e57	−	3.16356e58i	0.00180810	−	0.0221536i
$733$	3.34888e59			0.227886			0.113943	−	0.993487i	$-0.463652\pi$
$733$	3.34888e59			0.227886			0.113943	+	0.993487i	$0.463652\pi$
$734$	−2.40465e60	−	9.79666e58i	−1.59014	−	0.0647830i
$735$			4.31880e58i			0.0277542i
$736$	2.34205e60	+	4.83517e59i	1.46272	+	0.301980i
$737$	−2.53205e60			−1.53693
$738$	2.41211e58	−	5.92066e59i	0.0142303	−	0.349290i
$739$		−	2.30458e60i		−	1.32147i	−0.750617	−	0.660737i	$-0.770244\pi$
$739$		−	2.30458e60i		−	1.32147i	0.750617	−	0.660737i	$-0.229756\pi$
$740$	−5.96208e59	−	4.86604e58i	−0.332301	−	0.0271212i
$741$	1.64499e59			0.0891213
$742$	−2.16954e60	−	8.83880e58i	−1.14258	−	0.0465491i
$743$			8.63936e59i			0.442300i	0.975240	+	0.221150i	$0.0709810\pi$
$743$			8.63936e59i			0.442300i	−0.975240	+	0.221150i	$0.929019\pi$
$744$	2.17866e57	−	1.77465e58i	0.00108432	−	0.00883246i
$745$	−2.79127e60			−1.35058
$746$	9.03460e58	−	2.21760e60i	0.0425005	−	1.04320i
$747$			2.22681e60i			1.01848i
$748$	5.97069e58	−	7.31555e59i	0.0265516	−	0.325322i
$749$	1.63512e60			0.707020
$750$	−9.01950e58	−	3.67459e57i	−0.0379224	−	0.00154498i
$751$		−	6.73001e59i		−	0.275155i	−0.990491	−	0.137577i	$-0.956068\pi$
$751$		−	6.73001e59i		−	0.275155i	0.990491	−	0.137577i	$-0.0439316\pi$
$752$	5.56918e59	−	3.38907e60i	0.221420	−	1.34743i
$753$	−3.70871e58			−0.0143393
$754$	−1.70870e58	+	4.19410e59i	−0.00642491	+	0.157703i
$755$			4.33986e60i			1.58705i
$756$	−1.44408e59	−	1.17861e58i	−0.0513611	−	0.00419191i
$757$	2.27589e60			0.787297			0.393648	−	0.919261i	$-0.371213\pi$
$757$	2.27589e60			0.787297			0.393648	+	0.919261i	$0.371213\pi$
$758$	2.46709e60	+	1.00510e59i	0.830102	+	0.0338188i
$759$		−	1.73392e59i		−	0.0567480i
$760$	−4.78920e60	−	5.87947e59i	−1.52467	−	0.187177i
$761$	−5.78168e60			−1.79051			−0.895254	−	0.445557i	$-0.853006\pi$
$761$	−5.78168e60			−1.79051			−0.895254	+	0.445557i	$0.853006\pi$
$762$	7.61289e57	−	1.86863e59i	0.00229348	−	0.0562948i
$763$		−	9.15678e59i		−	0.268366i
$764$	−3.88949e59	+	4.76556e60i	−0.110900	+	1.35879i
$765$	1.38686e60			0.384718
$766$	6.29870e59	+	2.56612e58i	0.169999	+	0.00692585i
$767$			4.34373e60i			1.14067i
$768$	−5.23031e58	+	1.54845e59i	−0.0133642	+	0.0395652i
$769$	1.03054e60			0.256219			0.128109	−	0.991760i	$-0.459109\pi$
$769$	1.03054e60			0.256219			0.128109	+	0.991760i	$0.459109\pi$
$770$	1.01548e59	−	2.49256e60i	0.0245678	−	0.603032i
$771$			1.32264e59i			0.0311387i
$772$	7.52291e59	+	6.13993e58i	0.172354	+	0.0140670i
$773$	7.49309e60			1.67067			0.835336	−	0.549739i	$-0.185273\pi$
$773$	7.49309e60			1.67067			0.835336	+	0.549739i	$0.185273\pi$
$774$	5.07660e60	+	2.06823e59i	1.10157	+	0.0448786i
$775$			1.55357e59i			0.0328092i
$776$	9.40044e59	−	7.65725e60i	0.193220	−	1.57390i
$777$	4.00076e58			0.00800389
$778$	6.85302e58	−	1.68211e60i	0.0133448	−	0.327555i
$779$			2.64192e60i			0.500763i
$780$	−2.95171e58	+	3.61656e59i	−0.00544612	+	0.0667281i
$781$	3.53507e60			0.634931
$782$	3.06204e60	+	1.24749e59i	0.535388	+	0.0218120i
$783$			5.18493e58i			0.00882563i
$784$	3.68391e60	+	6.05368e59i	0.610481	+	0.100319i
$785$	−4.71760e60			−0.761129
$786$	7.07155e57	−	1.73575e59i	0.00111081	−	0.0272656i
$787$		−	7.15773e60i		−	1.09473i	−0.836895	−	0.547364i	$-0.815631\pi$
$787$		−	7.15773e60i		−	1.09473i	0.836895	−	0.547364i	$-0.184369\pi$
$788$	−8.03048e60	−	6.55420e59i	−1.19589	−	0.0976043i
$789$	−2.61065e59			−0.0378557
$790$	3.48375e60	+	1.41930e59i	0.491902	+	0.0200403i
$791$		−	6.00127e60i		−	0.825158i
$792$	−6.73246e60	−	8.26512e59i	−0.901457	−	0.110668i
$793$	−6.09155e60			−0.794312
$794$	−2.20476e59	+	5.41170e60i	−0.0279982	+	0.687232i
$795$			6.71698e59i			0.0830739i
$796$	−9.32184e59	+	1.14215e61i	−0.112286	+	1.37578i
$797$	2.72818e60			0.320072			0.160036	−	0.987111i	$-0.448839\pi$
$797$	2.72818e60			0.320072			0.160036	+	0.987111i	$0.448839\pi$
$798$	3.22444e59	+	1.31365e58i	0.0368462	+	0.00150113i
$799$		−	4.40127e60i		−	0.489887i
$800$	2.87132e59	−	1.39080e60i	0.0311309	−	0.150791i
$801$	−3.59738e60			−0.379930
$802$	−6.48226e59	+	1.59111e61i	−0.0666906	+	1.63696i
$803$		−	6.64672e60i		−	0.666164i
$804$	7.20131e59	+	5.87746e58i	0.0703128	+	0.00573869i
$805$	1.04157e61			0.990774
$806$	−3.42856e60	−	1.39681e59i	−0.317743	−	0.0129450i
$807$		−	5.83074e59i		−	0.0526477i
$808$	−1.45820e60	+	1.18780e61i	−0.128286	+	1.04497i
$809$	−1.66670e61			−1.42869			−0.714345	−	0.699794i	$-0.753275\pi$
$809$	−1.66670e61			−1.42869			−0.714345	+	0.699794i	$0.753275\pi$
$810$	5.20802e59	−	1.27834e61i	0.0434998	−	1.06773i
$811$		−	2.66643e60i		−	0.217016i	−0.994096	−	0.108508i	$-0.965393\pi$
$811$		−	2.66643e60i		−	0.217016i	0.994096	−	0.108508i	$-0.0346074\pi$
$812$	−6.69862e58	+	8.20744e59i	−0.00531262	+	0.0650925i
$813$	−5.06885e59			−0.0391749
$814$	3.74610e60	+	1.52618e59i	0.282142	+	0.0114946i
$815$			7.70589e60i			0.565605i
$816$	−3.39621e58	+	2.06673e59i	−0.00242941	+	0.0147840i
$817$	−2.26528e61			−1.57928
$818$	5.94082e58	−	1.45821e60i	0.00403671	−	0.0990833i
$819$			1.38910e61i			0.919969i
$820$	−5.80833e60	−	4.74055e59i	−0.374939	−	0.0306012i
$821$	2.32130e61			1.46058			0.730291	−	0.683137i	$-0.239385\pi$
$821$	2.32130e61			1.46058			0.730291	+	0.683137i	$0.239385\pi$
$822$	2.44227e59	+	9.94995e57i	0.0149791	+	0.000610257i
$823$		−	1.98399e61i		−	1.18616i	−0.805144	−	0.593079i	$-0.797912\pi$
$823$		−	1.98399e61i		−	1.18616i	0.805144	−	0.593079i	$-0.202088\pi$
$824$	−2.31852e61	−	2.84634e60i	−1.35126	−	0.165888i
$825$	−1.02967e59			−0.00585012
$826$	−3.46880e59	+	8.51437e60i	−0.0192131	+	0.471598i
$827$		−	2.48134e61i		−	1.33990i	−0.742408	−	0.669948i	$-0.766316\pi$
$827$		−	2.48134e61i		−	1.33990i	0.742408	−	0.669948i	$-0.233684\pi$
$828$	2.30378e60	−	2.82269e61i	0.121284	−	1.48602i
$829$	2.60612e61			1.33767			0.668836	−	0.743410i	$-0.266793\pi$
$829$	2.60612e61			1.33767			0.668836	+	0.743410i	$0.266793\pi$
$830$	2.18819e61	+	8.91481e59i	1.09508	+	0.0446141i
$831$			3.49598e59i			0.0170587i
$832$	3.04353e61	+	7.58714e60i	1.44806	+	0.360984i
$833$	4.78417e60			0.221953
$834$	5.33576e58	−	1.30969e60i	0.00241384	−	0.0592492i
$835$			2.21957e61i			0.979159i
$836$	3.01418e61	+	2.46007e60i	1.29670	+	0.105832i
$837$	−4.23854e59			−0.0177820
$838$	−3.27036e61	−	1.33236e60i	−1.33804	−	0.0545126i
$839$			4.27167e61i			1.70450i	0.523135	+	0.852250i	$0.324762\pi$
$839$			4.27167e61i			1.70450i	−0.523135	+	0.852250i	$0.675238\pi$
$840$	−8.67390e58	+	7.06544e59i	−0.00337559	+	0.0274963i
$841$	−2.60514e61			−0.988815
$842$	1.14267e60	−	2.80475e61i	0.0423025	−	1.03834i
$843$		−	8.75542e59i		−	0.0316153i
$844$	4.63002e59	−	5.67290e60i	0.0163077	−	0.199809i
$845$	3.83711e61			1.31830
$846$	−4.06398e61	−	1.65569e60i	−1.36199	−	0.0554882i
$847$		−	3.25345e60i		−	0.106363i
$848$	5.72955e61	+	9.41523e60i	1.82729	+	0.300274i
$849$	−1.57483e60			−0.0489973
$850$	7.40810e58	−	1.81836e60i	0.00224858	−	0.0551929i
$851$			1.56539e61i			0.463555i
$852$	−1.00540e60	−	8.20571e58i	−0.0290474	−	0.00237074i
$853$	−3.79541e61			−1.06986			−0.534932	−	0.844895i	$-0.679663\pi$
$853$	−3.79541e61			−1.06986			−0.534932	+	0.844895i	$0.679663\pi$
$854$	−1.19404e61	−	4.86457e59i	−0.328400	−	0.0133792i
$855$			5.71421e61i			1.53344i
$856$	−4.33991e61	−	5.32790e60i	−1.13640	−	0.139511i
$857$	2.39584e61			0.612153			0.306076	−	0.952007i	$-0.400984\pi$
$857$	2.39584e61			0.612153			0.306076	+	0.952007i	$0.400984\pi$
$858$	9.25772e58	−	2.27236e60i	0.00230819	−	0.0566558i
$859$			1.17173e61i			0.285083i	0.989789	+	0.142542i	$0.0455275\pi$
$859$			1.17173e61i			0.285083i	−0.989789	+	0.142542i	$0.954473\pi$
$860$	4.06474e60	−	4.98029e61i	0.0965083	−	1.18246i
$861$	3.89759e59			0.00903087
$862$	−1.79514e61	−	7.31351e59i	−0.405926	−	0.0165376i
$863$		−	1.26928e61i		−	0.280111i	−0.990144	−	0.140056i	$-0.955272\pi$
$863$		−	1.26928e61i		−	0.280111i	0.990144	−	0.140056i	$-0.0447281\pi$
$864$	3.79446e60	+	7.83367e59i	0.0817262	+	0.0168724i
$865$	−3.20181e61			−0.673065
$866$	2.06510e60	−	5.06890e61i	0.0423706	−	1.04001i
$867$		−	1.81693e60i		−	0.0363862i
$868$	−6.70935e60	−	5.47594e59i	−0.131149	−	0.0107040i
$869$	−2.18529e61			−0.416959
$870$	2.54529e59	+	1.03696e58i	0.00474059	+	0.000193134i
$871$		−	1.38664e62i		−	2.52106i
$872$	−2.98366e60	+	2.43038e61i	−0.0529545	+	0.431348i
$873$	−9.13621e61			−1.58295
$874$	−5.13996e60	+	1.26163e62i	−0.0869400	+	2.13400i
$875$			3.39863e61i			0.561221i
$876$	−1.54286e59	+	1.89037e60i	−0.00248736	+	0.0304763i
$877$	9.79868e61			1.54233			0.771163	−	0.636637i	$-0.219675\pi$
$877$	9.79868e61			1.54233			0.771163	+	0.636637i	$0.219675\pi$
$878$	−4.31238e61	−	1.75688e60i	−0.662723	−	0.0269997i
$879$			2.18316e60i			0.0327582i
$880$	−1.08171e61	+	6.58263e61i	−0.158480	+	0.964413i
$881$	1.01738e61			0.145543			0.0727713	−	0.997349i	$-0.476816\pi$
$881$	1.01738e61			0.145543			0.0727713	+	0.997349i	$0.476816\pi$
$882$	1.79973e60	−	4.41753e61i	0.0251400	−	0.617077i
$883$		−	1.19310e62i		−	1.62743i	−0.581266	−	0.813714i	$-0.697442\pi$
$883$		−	1.19310e62i		−	1.62743i	0.581266	−	0.813714i	$-0.302558\pi$
$884$	4.00626e61	+	3.26977e60i	0.533632	+	0.0435531i
$885$	2.63609e60			0.0342887
$886$	8.30207e61	+	3.38230e60i	1.05458	+	0.0429640i
$887$			1.36184e62i			1.68939i	0.535250	+	0.844694i	$0.320218\pi$
$887$			1.36184e62i			1.68939i	−0.535250	+	0.844694i	$0.679782\pi$
$888$	−1.06188e60	−	1.30361e59i	−0.0128647	−	0.00157934i
$889$	−7.04115e61			−0.833118
$890$	−1.44017e60	+	3.53499e61i	−0.0166427	+	0.408506i
$891$			8.01875e61i			0.905054i
$892$	−8.90796e58	+	1.09144e60i	−0.000982011	+	0.0120320i
$893$	1.81343e62			1.95263
$894$	−4.98796e60	−	2.03212e59i	−0.0524609	−	0.00213728i
$895$		−	1.94685e62i		−	2.00009i
$896$	5.90520e61	+	1.73025e61i	0.592606	+	0.173636i
$897$	9.49555e60			0.0930848
$898$	−1.41598e60	+	3.47562e61i	−0.0135599	+	0.332835i
$899$			2.40897e60i			0.0225360i
$900$	−1.67623e61	−	1.36808e60i	−0.153193	−	0.0125031i
$901$	7.44077e61			0.664350
$902$	3.64950e61	+	1.48682e60i	0.318344	+	0.0129695i
$903$			3.34194e60i			0.0284811i
$904$	−1.95546e61	+	1.59285e62i	−0.162822	+	1.32629i
$905$	−1.77488e62			−1.44394
$906$	−3.15955e59	+	7.75529e60i	−0.00251150	+	0.0616462i
$907$		−	2.10235e62i		−	1.63287i	−0.577437	−	0.816435i	$-0.695947\pi$
$907$		−	2.10235e62i		−	1.63287i	0.577437	−	0.816435i	$-0.304053\pi$
$908$	1.25487e61	−	1.53751e62i	0.0952345	−	1.16685i
$909$	1.41721e62			1.05098
$910$	1.36502e62	+	5.56114e60i	0.989164	+	0.0402991i
$911$			1.30080e61i			0.0921140i	0.998939	+	0.0460570i	$0.0146656\pi$
$911$			1.30080e61i			0.0921140i	−0.998939	+	0.0460570i	$0.985334\pi$
$912$	−8.51544e60	−	1.39932e60i	−0.0589272	−	0.00968336i
$913$	−1.37261e62			−0.928240
$914$	1.31293e60	−	3.22267e61i	0.00867705	−	0.212983i
$915$			3.69680e60i			0.0238772i
$916$	−1.72688e62	−	1.40942e61i	−1.09008	−	0.0889682i
$917$	−6.54047e61			−0.403509
$918$	4.96095e60	+	2.02111e59i	0.0299136	+	0.00121869i
$919$			5.61608e60i			0.0330984i	0.999863	+	0.0165492i	$0.00526802\pi$
$919$			5.61608e60i			0.0330984i	−0.999863	+	0.0165492i	$0.994732\pi$
$920$	−2.76452e62	−	3.39386e61i	−1.59248	−	0.195501i
$921$	−8.92423e60			−0.0502479
$922$	2.60758e60	−	6.40046e61i	0.0143512	−	0.352259i
$923$			1.93593e62i			1.04149i
$924$	3.62931e59	−	4.44679e60i	0.00190859	−	0.0233849i
$925$	9.29591e60			0.0477876
$926$	1.44825e62	+	5.90023e60i	0.727800	+	0.0296509i
$927$			2.76633e62i			1.35903i
$928$	4.45226e60	−	2.15658e61i	0.0213832	−	0.103576i
$929$	5.82307e61			0.273415			0.136707	−	0.990611i	$-0.456348\pi$
$929$	5.82307e61			0.273415			0.136707	+	0.990611i	$0.456348\pi$
$930$	−8.47687e58	+	2.08070e60i	−0.000389129	+	0.00955141i
$931$			1.97119e62i			0.884679i
$932$	−1.33738e62	−	1.09152e61i	−0.586840	−	0.0478958i
$933$	6.03323e60			0.0258842
$934$	−3.11545e60	−	1.26925e59i	−0.0130688	−	0.000532430i
$935$			8.54863e61i			0.350633i
$936$	4.52628e61	−	3.68694e62i	0.181530	−	1.47868i
$937$	−2.38610e62			−0.935745			−0.467872	−	0.883796i	$-0.654979\pi$
$937$	−2.38610e62			−0.935745			−0.467872	+	0.883796i	$0.654979\pi$
$938$	1.10734e61	−	2.71803e62i	0.0424640	−	1.04230i
$939$		−	8.73767e60i		−	0.0327656i
$940$	−3.25395e61	+	3.98688e62i	−0.119323	+	1.46200i
$941$	−1.85072e62			−0.663681			−0.331840	−	0.943336i	$-0.607670\pi$
$941$	−1.85072e62			−0.663681			−0.331840	+	0.943336i	$0.607670\pi$
$942$	−8.43030e60	−	3.43455e59i	−0.0295647	−	0.00120448i
$943$			1.52502e62i			0.523034i
$944$	3.69502e61	−	2.24857e62i	0.123938	−	0.754213i
$945$	1.68749e61			0.0553572
$946$	−1.27486e61	+	3.12922e62i	−0.0409024	+	1.00397i
$947$		−	4.89543e61i		−	0.153618i	−0.997046	−	0.0768088i	$-0.975527\pi$
$947$		−	4.89543e61i		−	0.153618i	0.997046	−	0.0768088i	$-0.0244731\pi$
$948$	6.21510e60	+	5.07255e59i	0.0190754	+	0.00155687i
$949$	3.63999e62			1.09272
$950$	7.49209e61	+	3.05232e60i	0.219992	+	0.00896260i
$951$		−	2.63781e60i		−	0.00757621i
$952$	7.82677e61	+	9.60855e60i	0.219891	+	0.0269949i
$953$	2.84020e62			0.780545			0.390273	−	0.920699i	$-0.372381\pi$
$953$	2.84020e62			0.780545			0.390273	+	0.920699i	$0.372381\pi$
$954$	2.79909e61	−	6.87054e62i	0.0752492	−	1.84704i
$955$		−	5.56883e62i		−	1.46451i
$956$	−4.75699e59	+	5.82847e60i	−0.00122382	+	0.0149947i
$957$	−1.59660e60			−0.00401834
$958$	−2.56428e61	−	1.04470e60i	−0.0631378	−	0.00257227i
$959$		−	9.20270e61i		−	0.221679i
$960$	4.60443e60	−	1.84704e61i	0.0108512	−	0.0435291i
$961$	4.14009e62			0.954594
$962$	−8.35792e60	+	2.05150e62i	−0.0188548	+	0.462802i
$963$			5.17814e62i			1.14294i
$964$	7.63187e62	+	6.22887e61i	1.64821	+	0.134521i
$965$	−8.79094e61			−0.185764
$966$	1.86127e61	+	7.58292e59i	0.0384849	+	0.00156789i
$967$		−	6.35991e62i		−	1.28675i	−0.765550	−	0.643376i	$-0.777533\pi$
$967$		−	6.35991e62i		−	1.28675i	0.765550	−	0.643376i	$-0.222467\pi$
$968$	−1.06011e61	+	8.63524e61i	−0.0209878	+	0.170959i
$969$	−1.10587e61			−0.0214242
$970$	−3.65759e61	+	8.97778e62i	−0.0693408	+	1.70201i
$971$			4.53603e62i			0.841536i	0.907168	+	0.420768i	$0.138239\pi$
$971$			4.53603e62i			0.841536i	−0.907168	+	0.420768i	$0.861761\pi$
$972$	5.60031e60	−	6.86174e61i	0.0101676	−	0.124578i
$973$	−4.93504e62			−0.876841
$974$	−6.76646e62	−	2.75669e61i	−1.17659	−	0.0479347i
$975$		−	5.63884e60i		−	0.00959606i
$976$	3.15335e62	+	5.18182e61i	0.525201	+	0.0863050i
$977$	−4.62850e62			−0.754491			−0.377246	−	0.926113i	$-0.623129\pi$
$977$	−4.62850e62			−0.754491			−0.377246	+	0.926113i	$0.623129\pi$
$978$	−5.61011e59	+	1.37704e61i	−0.000895067	+	0.0219700i
$979$		−	2.21743e62i		−	0.346268i
$980$	−4.33372e62	−	3.53703e61i	−0.662390	−	0.0540619i
$981$	2.89979e62			0.433828
$982$	−4.09611e62	−	1.66877e61i	−0.599832	−	0.0244375i
$983$		−	3.44664e62i		−	0.494052i	−0.969009	−	0.247026i	$-0.920547\pi$
$983$		−	3.44664e62i		−	0.494052i	0.969009	−	0.247026i	$-0.0794532\pi$
$984$	−1.03449e61	−	1.27000e60i	−0.0145154	−	0.00178199i
$985$	9.38406e62			1.28893
$986$	1.14870e60	−	2.81955e61i	0.00154451	−	0.0379109i
$987$		−	2.67533e61i		−	0.0352142i
$988$	−1.34722e62	+	1.65068e63i	−0.173598	+	2.12699i
$989$	−1.30761e63			−1.64952
$990$	7.89351e62	+	3.21585e61i	0.974834	+	0.0397152i
$991$		−	1.02331e63i		−	1.23725i	−0.785685	−	0.618627i	$-0.787689\pi$
$991$		−	1.02331e63i		−	1.23725i	0.785685	−	0.618627i	$-0.212311\pi$
$992$	1.76294e62	+	3.63960e61i	0.208686	+	0.0430832i
$993$	−4.00107e61			−0.0463705
$994$	−1.54599e61	+	3.79473e62i	−0.0175425	+	0.430592i
$995$		−	1.33467e63i		−	1.48282i
$996$	3.90379e61	+	3.18614e60i	0.0424659	+	0.00346592i
$997$	−1.26108e61			−0.0134321			−0.00671606	−	0.999977i	$-0.502138\pi$
$997$	−1.26108e61			−0.0134321			−0.00671606	+	0.999977i	$0.502138\pi$
$998$	−1.40668e63	−	5.73090e61i	−1.46708	−	0.0597697i
$999$			2.53616e61i			0.0259001i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4.43.b.a.3.9	✓	20
4.3	odd	2	inner	4.43.b.a.3.10	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4.43.b.a.3.9	✓	20	1.1	even	1	trivial
4.43.b.a.3.10	yes	20	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4 = 2^{2} \)
Weight:	\( k \)	\(=\)	\( 43 \)
Character orbit:	\([\chi]\)	\(=\)	4.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(85368.2 - 2.09541e6i) q^{2} +4.36838e8i q^{3} +(-4.38347e12 - 3.57763e11i) q^{4} +5.12233e14 q^{5} +(9.15355e14 + 3.72920e13i) q^{6} -3.44914e17i q^{7} +(-1.12387e18 + 9.15464e18i) q^{8} +1.09228e20 q^{9} +O(q^{10})\)	\(q+(85368.2 - 2.09541e6i) q^{2} +4.36838e8i q^{3} +(-4.38347e12 - 3.57763e11i) q^{4} +5.12233e14 q^{5} +(9.15355e14 + 3.72920e13i) q^{6} -3.44914e17i q^{7} +(-1.12387e18 + 9.15464e18i) q^{8} +1.09228e20 q^{9} +(4.37284e19 - 1.07334e21i) q^{10} +6.73283e21i q^{11} +(1.56285e20 - 1.91486e21i) q^{12} -3.68714e23 q^{13} +(-7.22737e23 - 2.94447e22i) q^{14} +2.23763e23i q^{15} +(1.90868e25 + 3.13649e24i) q^{16} +2.47874e25 q^{17} +(9.32461e24 - 2.28878e26i) q^{18} +1.02130e27i q^{19} +(-2.24536e27 - 1.83258e26i) q^{20} +1.50671e26 q^{21} +(1.41081e28 + 5.74770e26i) q^{22} +5.89536e28i q^{23} +(-3.99909e27 - 4.90949e26i) q^{24} +3.50090e28 q^{25} +(-3.14765e28 + 7.72609e29i) q^{26} +9.55133e28i q^{27} +(-1.23397e29 + 1.51192e30i) q^{28} +5.42849e29 q^{29} +(4.68875e29 + 1.91022e28i) q^{30} +4.43764e30i q^{31} +(8.20166e30 - 3.97270e31i) q^{32} -2.94115e30 q^{33} +(2.11606e30 - 5.19398e31i) q^{34} -1.76676e32i q^{35} +(-4.78798e32 - 3.90778e31i) q^{36} +2.65529e32 q^{37} +(2.14005e33 + 8.71866e31i) q^{38} -1.61068e32i q^{39} +(-5.75684e32 + 4.68931e33i) q^{40} +2.58682e33 q^{41} +(1.28625e31 - 3.15719e32i) q^{42} +2.21804e34i q^{43} +(2.40876e33 - 2.95132e34i) q^{44} +5.59503e34 q^{45} +(1.23532e35 + 5.03276e33i) q^{46} -1.77561e35i q^{47} +(-1.37014e33 + 8.33784e33i) q^{48} +1.93008e35 q^{49} +(2.98866e33 - 7.33583e34i) q^{50} +1.08281e34i q^{51} +(1.61625e36 + 1.31913e35i) q^{52} +3.00183e36 q^{53} +(2.00140e35 + 8.15380e33i) q^{54} +3.44878e36i q^{55} +(3.15756e36 + 3.87639e35i) q^{56} -4.46143e35 q^{57} +(4.63421e34 - 1.13749e36i) q^{58} -1.17807e37i q^{59} +(8.00541e34 - 9.80857e35i) q^{60} +1.65211e37 q^{61} +(9.29869e36 + 3.78833e35i) q^{62} -3.76743e37i q^{63} +(-8.25444e37 - 2.05773e37i) q^{64} -1.88868e38 q^{65} +(-2.51081e35 + 6.16294e36i) q^{66} +3.76074e38i q^{67} +(-1.08655e38 - 8.86802e36i) q^{68} -2.57531e37 q^{69} +(-3.70210e38 - 1.50825e37i) q^{70} -5.25049e38i q^{71} +(-1.22758e38 + 9.99945e38i) q^{72} -9.87210e38 q^{73} +(2.26677e37 - 5.56393e38i) q^{74} +1.52932e37i q^{75} +(3.65384e38 - 4.47684e39i) q^{76} +2.32225e39 q^{77} +(-3.37505e38 - 1.37501e37i) q^{78} +3.24571e39i q^{79} +(9.77690e39 + 1.60661e39i) q^{80} +1.19099e40 q^{81} +(2.20832e38 - 5.42045e39i) q^{82} +2.03868e40i q^{83} +(-6.60463e38 - 5.39047e37i) q^{84} +1.26969e40 q^{85} +(4.64770e40 + 1.89350e39i) q^{86} +2.37137e38i q^{87} +(-6.16367e40 - 7.56684e39i) q^{88} -3.29345e40 q^{89} +(4.77637e39 - 1.17239e41i) q^{90} +1.27175e41i q^{91} +(2.10914e40 - 2.58421e41i) q^{92} -1.93853e39 q^{93} +(-3.72063e41 - 1.51581e40i) q^{94} +5.23144e41i q^{95} +(1.73543e40 + 3.58279e39i) q^{96} -8.36434e41 q^{97} +(1.64768e40 - 4.04432e41i) q^{98} +7.35415e41i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 802164 q^{2} + 1311168818192 q^{4} + 139235684997000 q^{5} + 68\!\cdots\!12 q^{6}+ \cdots - 73\!\cdots\!76 q^{9}+O(q^{10}) \) 20 * q + 802164 * q^2 + 1311168818192 * q^4 + 139235684997000 * q^5 + 6838718638036512 * q^6 - 27661415389266953664 * q^8 - 733170595646091132876 * q^9	\( 20 q + 802164 q^{2} + 1311168818192 q^{4} + 139235684997000 q^{5} + 68\!\cdots\!12 q^{6}+ \cdots + 18\!\cdots\!96 q^{98}+O(q^{100}) \) 20 * q + 802164 * q^2 + 1311168818192 * q^4 + 139235684997000 * q^5 + 6838718638036512 * q^6 - 27661415389266953664 * q^8 - 733170595646091132876 * q^9 + 42625185369378343240 * q^10 - 25848729272513843675520 * q^12 - 144898631886191567496248 * q^13 - 306990738295992471121728 * q^14 + 27792040878005009897120000 * q^16 + 81746542725793625328399528 * q^17 - 217831601203830755951030124 * q^18 + 6344592401135696008447573920 * q^20 + 7651089590961386749851047424 * q^21 - 46254109397133274566238240800 * q^22 + 506607644284406956508290140672 * q^24 + 844166434154191999887370985820 * q^25 + 305910330554143989456096580488 * q^26 - 1621415041794921570009743366400 * q^28 + 8494173617816210057524981535304 * q^29 + 32483836243012295467926394800960 * q^30 - 117067340157863901568162598132736 * q^32 - 195434629079924022845409037850880 * q^33 - 435728002928020507520645688017048 * q^34 + 905808650859207966395798479569552 * q^36 + 320827308804868360600766816935048 * q^37 - 834801746373065199942054885540960 * q^38 - 2080347678511686114819737054821760 * q^40 + 12238592465130696350192985088255080 * q^41 + 39180793491987624842407723014766080 * q^42 - 40147560736600746149658671246198400 * q^44 - 57674168870802092374169153418160440 * q^45 - 133593585977858896021440512714708928 * q^46 + 223617847456028179696661192651827200 * q^48 - 763663932888918132103393205670102316 * q^49 - 1073296820241355924814923786366326660 * q^50 - 580677968103327319151855528386839392 * q^52 + 3592528655430046000719727125882705672 * q^53 + 8087462166590362832897538370358812224 * q^54 - 4056862272141293872664295528725971968 * q^56 + 1376964140105307936676325853454767360 * q^57 - 17787847411919404506009575679670206968 * q^58 + 27803845757503537955964429994460432640 * q^60 - 72876803820111699199759396563493728440 * q^61 - 83779848218915601601226708273126396160 * q^62 - 51258837764961549702163120437185671168 * q^64 + 143337782114217802520090675036041365840 * q^65 + 479881795533282188176080436671310498560 * q^66 - 201679039132028748396903074185205050848 * q^68 + 496255895990320623770556878095159325184 * q^69 + 244550326432622351468933399511720393600 * q^70 + 1389470702024602675984554222025462031424 * q^72 + 675217186810136917874725959945538619752 * q^73 - 5048325762233564608985375515346235670968 * q^74 - 727730227778639944706768217921060021120 * q^76 - 13945771646073577607404274150247166932480 * q^77 + 2630485389052859541031650397045824087360 * q^78 - 14080069438753558698176635521889841825280 * q^80 + 50326416439524122225413610454605570342484 * q^81 + 38442316210858292795461617709768475559208 * q^82 + 21041665749991691364416236667734761560064 * q^84 - 100747029416581567610441680879732008651760 * q^85 - 109399875737541346773887857542693387248928 * q^86 + 61542411942227832459784035156153652876800 * q^88 + 298677519739918601751826215340976530195944 * q^89 + 5248331693055749298139854308097091987080 * q^90 - 311056321102768653749854891753699429405440 * q^92 - 902946967697899772252214392286633142732800 * q^93 - 120754391334239789606838050760853185629568 * q^94 - 369891338439189821551415861997759233875968 * q^96 + 2729077788738058742150638081801454021515048 * q^97 + 1829330555781863715528793474157579946873396 * q^98

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